Social Security

Yes.  People who get SSDI can work and keep their full SSDI check if they stay under substantial gainful activity.  The SSDI work rules are complicated but they allow you to try out work before deciding that you are no longer disabled.  People on SSDI can test out their ability to work with a trial work period before they move into the substantial gainful activity standard.  Refer to Social Security's Redbook for more information on working while on SSDI benefits, trial work periods and substantial gainful activity,

There are different rules for people who get SSI and SSDI benefits.  Refer to Social Security's Redbook for the most up-to-date information.