Is it safe to eat sliced ham that has gone soft and mushy?

This is a difficult question to answer, sliced ham should not be soft and mushy, so it is perhaps better not to eat it.

However if the ham has been cooked properly and stored in a cool place since being cooked (and if it is from a shop, is still within is use by date) it should be OK to eat. It may be that it had too much water in it when it was packed.

On balance however if food does not look OK, is out of date, has not been stored at the correct temperature and certainly if it smells bad - it is safer not to eat it.