单引号和$ in string bash

Im running the below script to run some checks on file paths within a function Some of the paths contains single quotes and the temporary files contain "$" If I enclose the variable in single quotes (name variable below) then the string in truncated if there is a ' in the file path. If I use a double quote around the filepath then it truncates if there is a "$" in the path. Is there any way out of this circular conundrum?Im running the below script to run some checks