As with all things, "it depends."
Section 8 is welfare. It's a program for poor people. So if you have a household that has been approved for a HUD voucher, we're assuming they are too poor--according to federal guidelines--to support themselves. Now, take that same household an add someone who makes $5000/month. Oops, you are no longer "poor" and therefore most likely no longer qualify for a voucher.
Now of course there are many "ifs." What IF the tenants never say anything to HUD and what IF the land lord never says anything and what IF the land lord agreeing not to say anything is based on the tenant handing him an extra $100 a month "cash under the table" and what IF the neighbor who is also on Sec 8 or is just a busy body finds out what's going on because your tenant was bragging about milking the system and reports you/your tenants to the housing authority, etc.
My view is honesty is always the best policy, even if it doesn't appear that there is any wrong-doing. I'd first tell the tenant that IF I approve this additional resident then I will be reporting it to Sec 8...then let the chips fall where they may.
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