Sans is a MONSTER and not a HUMAN, so he doesn't follow HUMAN biology like a HUMAN skeleton. Same with Gaster and Papyrus.  

Things that are said from the past (in the long paragraphs) is written in italics, in case that isn't clear.

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She still thought it could have been handled better - this whole situation. The fact that Frisk was actually the one who was in charge of the entirety of the Mafia, was something that was bound to keep her up at night, with the amount that she worried and stressed, about the well being of her children. Frisk was like a daughter to Toriel, and always had been ever since she had been a part of  the family, since being roped into all of this from the very beginning, so how could she not worry about her? She worried about her happiness, she worried about her relationship with the skeleton she loved.

At first, Toriel had been extremely skeptical about her daughter's relationship with that skeleton monster, but as time went on, it was very clear to the goat woman just how much those two actually adored each other. It was nice, seeing the way they smiled at each other; especially Sans. Toriel wasn't sure she had actually ever seen him that happy, at least not since he had been an innocent child. To think that putting this pressure on her could cripple her future with him, it made her feel guilt. Guilt, that she didn't step up and have more to say on the subject. She had wanted to say: absolutely not, about Frisk being the Mafia boss. In fact, that is what she said on the subject, however, the human had not wanted to hear it. 

Because Frisk was an adult with the free will to think for herself and do as she pleased, Toriel could only do so much to dictate how her life went. She knew, even as a protective mother, that she could not make Frisk's decisions for her, and she couldn't stop her from doing certain things. The adult human had been pretty set on taking the place of Asgore, and no matter how much she didn't accept it, Frisk would not step down. Maybe it had been selfish of her, to expect Asgore to quit his job, to step down, to spend more time with her. Perhaps she had thought more about how this would affect others, rather than just thinking about herself and how she wanted to save her own marriage.

Just thinking that, the goat women let out a soft sigh, as she was sitting in one of her cosy living room chairs, with an open book resting on her lap, which she had long forgotten about since getting so roped within her thoughts. It wasn't until she heard the sound of her husband clearing her throat, that she actually traveled back to reality, and her gaze became fixated upon him, standing beside her chair, offering a cup of tea with a warm smile. For a moment, she blinked, as if still being far away in fairy land, until she faintly smiled, and decided to take the mug from his grasp. 

"Thank you..." Toriel said. 

"It is no problem, my dear." Asgore spoke, going to kneel down a little, to lightly nuzzle against Toriel's furry cheek. It did earn a small laugh out of the goat woman, as it was admittedly nice to have her husband having him spend more time with her again. It had been nice, actually feeling her husband's big, strong arms encircle her in a protective cuddle while they slept at night, rather than finding herself alone beneath the covers. At first, being alone was something she had become accustomed to, when she was getting sick of her husband's lack of free time. But... Then it started to get to a point where she... Missed him. It was lonely. And she had wanted him back.

"...Don't you think we could have done more?" Toriel asked towards Asgore, who had gone to sit upon the empty couch. When she had said that, Asgore made a comment, saying that she sounded perturbed, and that was putting it lightly. Actually, she said that last bit out loud, with yet another sad chuckle, as she stared thoughtfully into her cup of tea. "All I am saying is... I think it was irresponsible. To allow Frisk to take your place. But I am not saying it is your fault. It is mine. I am the one who wanted you to quit, after all." She pointed out. 

"But it was only right for you to want that." Asgore replied. "You were right, Tori. These past couple of years, I have not paid enough attention to you, or the children." The goat man continued, while trying his best to keep on a smile, but due to the current subject matter, it looked like a smile that was more bittersweet than it was happy. "...I do think the position could have been handed down to someone more... Suitable. But I could never force someone like... For example, Gaster, to take it, if he did not want it." Like many others, he had a life of his own to lead, and if he had wanted to be the Mafia boss, he might have said something.

That was the thing, Asgore had once seen Gaster being the one who would possibly be the next to lead, say if something were to happen to himself, or if he had decided that he wasn't right for the job anymore. In fact, he and Gaster had probably had a conversation about it at one point, but that was before he had sadly lost his wife, and needed to piece his life back together. 

"You said you had wanted to speak to me?" Gaster had said, stepping into the office that belonged to the goat man, who was not only his boss, but was of course a good friend. Due to the fact that they shared a friendship, it was likely the huge reason why Asgore trusted him. He trusted him, so much more compared to anyone else that worked for him. Ever since joining the Mafia, Gaster was a loyal skeleton, and a good friend. 

"Ah, yes, Gaster. Please, take a seat." Asgore spoke, directing him to sit in the chair, that sat unoccupied, opposite his desk. Waiting for the skeleton to sit down, the goat proceeded to continue. "You're probably unaware as to why I wanted to talk to you. You are not in any trouble, in case you were concerned." Asgore chuckled, seeing the look of slight worry on Gaster's face. 

That was the thing about him, it probably wasn't until his wife - Lucida - died, that he really started to master the poker face, and it was a quality that he would likely carry for the rest of his life. It was something that Asgore still saw in him to this day, where sometimes he was difficult to read, because he always had that blank look that didn't really show you what he was feeling or thinking. Not that it was worrying, like it had been when he had lost his wife. Nowadays, it only seemed more like a habit that was hammered into him so much that it was just part of who he was now. If Gaster felt the need to talk, he would just talk - especially to that flame monster he adored. 

"I only wanted to talk to you, as you see, you have been doing a very good job ever since coming here, and I know that you have a family to provide for. Your wife - your two sons..." Asgore nattered on, while the skeleton continued to listen, nodding every now and then as he was seeming to take in what he was saying. "What I am saying is: I would like to make an offer. Because you're my dear friend, and I trust you, I wonder how you would feel if I said I would feel delighted if you were the next person to become this organisation's boss, say if anything were to happen to me, or if I were to step down." 

"W-Wait, what?" Gaster stammered out. "Me? Not that I do not feel honored, but... It is a big responsibility." The skeleton answered, not even sure how to wrap his mind around the fact that he was even being offered such a position if it were to come up. When joining this group, because he wanted to be able to take care of his family, he never saw it becoming more than it already was. All it was to him, was a way to gain money, and to spend time with good friends, like Grillby for example. For it to become an even bigger responsibility... 

"Of course, you don't have to accept. I am in no way insinuating that you are expected to say yes. After all, it is only an offer." 

"I..." Gaster started, until he paused, seeming to think about it. Matter of fact, he thought about it for a long while, as the two of them sat in silence. Not that the goat really minded, he knew that it was likely a lot to think about. Finally, Gaster did seem to make his decision, after some stretching minutes of silence. "I would be glad to accept." Gaster said with a confident expression on his face. Asgore had asked him if he was sure, at least several times, and of course, every time he said yes.

But then, things changed. Gaster lost his wife, and became a complete and utter mess. His son - Sans - did not seem like he would enjoy the idea of being a boss, because at the time he had been more focused on just doing missions. That was made much more obvious when Gaster had been taken from them, and Sans didn't want to be involved with anyone. So much was different since back then. Gaster may have made the decision back then, but now that he had Grillby, and the possibility for a better future, he might not be so rash.

"I only hope that if it becomes too much for Frisk, that she steps down. Because I do not want her ruining her own happiness for the well being of others." Toriel shook her head. She understood wanting to do good things for other people, but sometimes it was more important to look out for yourself. It's no good, to not take care of yourself, and to continuously put yourself second to everyone else. Frisk only deserved happiness. 

As the boss, holding onto happiness felt like it wasn't practical.