To fix a worn-out cassette tape, you can try the following DIY methods:
1. Run the backside of the tape over a rounded surface, such as a pen, to re-flatten it as best as possible.
2. Carefully align and reattach the strand ends against a backing of special Mylar splicing tape, then trim the excess off either side.
However, for the best results and to ensure the preservation of the tape's sound quality, it is recommended to digitize the cassette tape. A professional film digitizing company like ScanCafe can use a state-of-the-art deck to capture the sound on both sides of the tape and save it as a digital file.