Thread breakage or shredding can be caused by a variety of factors in the Brother PE535 Embroidery Machine. Here are some steps to help fix the issue:

1. Check the thread tension: If the thread tension is too tight or too loose, it can cause thread breakage or shredding. Make sure the thread tension is set correctly for the type of fabric and thread you are using.
2. Change the needle: A damaged or bent needle can cause thread breakage or shredding. Change the needle regularly and make sure you are using the correct needle for the type of fabric and thread you are using.
3. Check the thread path: Check that the thread is correctly threaded through the machine and the needle. Make sure there are no obstructions or tangles in the thread path.
4. Clean the machine: Build-up of lint and debris can cause thread breakage or shredding. Clean the machine regularly, particularly around the needle area and the bobbin case.
5. Use high-quality thread: Poor quality thread can cause thread breakage or shredding. Use high-quality embroidery thread that is suitable for your machine and the type of fabric you are using.
6. Slow down the embroidery speed: Running the machine too fast can cause thread breakage or shredding. Slow down the embroidery speed to reduce the strain on the thread.

By following these steps, you should be able to fix the thread breakage or shredding issue in your Brother PE535 Embroidery Machine.