1. You’re happy with what your earn and they offer you something you’re happy with = win
2. You’re not happy with what you earn and they try and lowball you because of your situation = lose
If it’s 2 then you’d look to leave soon anyway. Do you really want to work somewhere that tries to exploit you when you’re in a position of weakness while overlooking the fact that an unhappy hire is most likely to leave in the near future?
If you don’t like what they propose then make a counter offer. Worst thing they can say is no.