I would never say something is impossible BUT there should be no reason why if you unprotected a cell, anyone else should be able to write into it.

I'm assuming;
you unprotected the cells using cell format or the lock icon and then
protected the worksheet.

Ask the person to send it back to you and see if you can write in the cells.

It's possible the file got corrupted somehow during emailing but very unlikely that it would open up still and have this specific problem.

Chemist B