Good grief, is that stuff still being sold?
It used to contain metallic salts and so when an oxidising colour or bleach was applied afterwards, it reacted with the metals left in the hair and some of hair would break off.
You need to do a test for metallic salts (incompatibility test). Also take tiny swatches from different areas of the head as one section might be ok but another area could be contaminated.
Incompatibility Test
Mix 1 part perm solution to 20 parts 6% (20 vol) liquid peroxide in a glass dish. Add the hair and wait 20 minutes.
If you see any of the following, she’ll need to use a good quality chelating shampoo to remove the metals present in the hair.
Bubbling
Fizzing
Heat
Colour change
A normal deep cleansing shampoo won’t be adequate.
Ideally, look out for a specific product for removing metallic salts that’s sold in most wholesalers. Malibu make one but I think other brands are available too.
Finally, maybe try to educate your sister-in-law about using off the shelf diy lightening kits. They usually end up leaving hair looking and feeling awful.