>>57069806Pokémon have the right to leave their Trainer for any reason regardless of the Trainers feelings. All the Trainer can do is disapprove at most.
It's also not like every instance of Pokémon falling in love is like what happened with those two Butterfree, the Pokémon may not leave.
If the two Pokémon belong to the same Trainer then it's not really much of a problem. If the two Pokémon belong to separate Trainers then there's a few ways that could go, but it seems generally the two Pokémon still stay with their Trainers. If one of the Pokémon has a Trainer and the other is a Wild Pokémon, the Trainer could have the Wild Pokémon join their team but sometimes like in the case shown in the OP image both Pokémon may instead want to leave.