If what is under the tiles is not hard, then you have no option but to remove it. The tiles will simply move and the grout or tiles will break up without a hard surface underneath.
I thought under those tiles should be a shower pan (probably a mud pan). There are several posts on replacing shower pans. Try a search (Your "Edit" menu "Find in Page" option from index level in this bullitin board) search for keywords such as "shower"
I don't know how a mud pan could become soft, but I'm not an expert. Could be the shower was not properly build? Wait for posts from others who know more than I.