Can a person earn wages under $8,000 while they are on Long Term Disability which is non-taxable?

Above $3500 you must file taxes. It may or may not be taxable by you deductions and it has nothing to do with Long Term Disability. If you thinking about SSA or SSDI then in most cases your allowed to earn some money before they start take money from you. In most cases that is under $700 a month. In some it is less in some it is more, but you still might pay taxes.