If a 4yo fell asleep before brushing her teeth, would you wake her up to brush her teeth? maybe just use some wet wipe while she sleeps?
In my experience, getting a 4yo who has fallen asleep from exhaustion, awake enough to effectively brush their teeth is too much effort to even contemplate it. Only if he wakes up enough to be coherent when we move him to his bed do we reconsider if he is awake enough to brush his teeth.
If it happens only rarely, then I believe it will not harm the child to skip brushing their teeth when they fall asleep before it.
If it starts to happen with some frequency, then you should start to look at changing the evening routine so that you can get their teeth brushed earlier.
When my son became the first tooth I wanted to start settle good routines with him. So before sleeping to clean the teeth is a duty we will not avoid.
When he was around 4 years old, he started to try to sneek away, for example after he did not need to brush the teeth if he falls asleep in time. He tried to bring intentional situations, where he falls asleep before teeth brushing. So I started to let not trick me.
Toothpaste for small children is made in a style, it is not a problem if the children swallow it. So for me it was clear to I clean the teeth, even if my son was to tired to get into the bathroom and wash out the mouth. In this case the toothpaste simple stayed in the mouth. But for my son was clear: brushing teeth is something really important.
And one point which was important for me too: if the bacteria grow in the mouth and the first teeth get ill, this will cause also damage in the (yet not grown) second teeth. The bacteria can reach them inside the flesh, so they may grow out already ill.