do they basically become worthless
No, it's fair to say that a vibrant, growing company's shares cannot just become worthless after it takes over another another company. In this case, it appears that Fox shareholders are getting a mix of cash and a new class of Disney shares for a portion of the Fox business. You will own a slightly smaller piece of a larger company. (Think about it, if you own a business and combine with another business of identical size, you and the other guy now own 1/2 of a business that's twice the size. In this case, the Fox acquisition is a smaller piece)
I've read the press release as well as a bit of the S4 and it appears your shares are not re-issued or swapped for the other class of shares.