So forgive me if i'm stretching a bit, but what if Gaster's focus of work was the resets, and he found a way to use them by using the Core's power as a substitution to Determination, and with these 'resets' he was able to bring back fallen monsters, but due to the resets not being as effective due to lack of Determination, the now brought back monsters were locked off from the world, forgotten, wondering the world as wandering shambles of their former selves.
This would explain their strange appearance and why most of them seem to look up to Gaster and his work, and it could explain why Sans has vivid memories after the reloads and resets, it could of been a result of a failed experiment that ended in Sans having low stats and Gaster being erased.
Then again, this is just a theory, nothing more.