I need to know how to write off work I did for people who never paid me?

[mikej-nichols]

I performed a couple of cases to do background research for a client, which I was out of pocket several hundred dollars on a couple of occasions and those clients have never paid my invoice

[MichaelMc]

I am assuming that you keep your business books using the cash method, recognizing income only when it is actually or constructively received and recognizing expenses when you pay them by cash, check, or credit card.

You cannot write-off your entire unpaid invoice as a business bad debt, because you had not previously recognized the income. 

However, you can deduct your actual expenses related to the work you did for that client, assigning the expenses to their appropriate categories (research materials, copies, travel, etc.).

If my initial assumption is not correct, and you keep your business books using the accrual method, recognizing income when you invoice the client, then you can, in the year a debt becomes uncollectible, take a deduction for the amount of the unpaid invoice amount as a business bad debt.