If your chain tip is on the dead side of a hard fork (i.e. if the majority of the network will predictably soon finish switching away from software which considers your chain tip valid, to software which considers your chain tip invalid), then nobody cares if your chain tip is the longest in the interrim, or how long you still hold out running the software that considers your chain tip valid. Your side of the fork no longer holds any economic value as a platform for transactions, so nobody will participate in it. You'll just be out there mining blocks all alone, blocks that say you earn all the virtual tokens, but where those tokens are worthless on your side of the fork.

It's a bit like how, in old pre *serv IRC networks, in cases of netsplits, you could end up on a partition of the network where you were the only one in a previously-moderated channel; and so you could effectively do whatever you wanted in that channel. But it didn't really matter, because nobody could hear you.