No, this is not true. There is no government program, benefit, or entitlement that pays a spouse simply for being married to an incarcerated person. This rumor circulates inside facilities and outside them, but it has no basis in law.
Where some confusion may come from is Social Security disability benefits. When someone receiving SSDI is incarcerated, their benefits are suspended after a certain period in custody. In some cases, a spouse may have previously been receiving spousal benefits tied to the incarcerated person's SSDI record, and there can be complicated interactions between disability payments and marriage that vary by individual circumstances. But none of that amounts to a $2,500 monthly check that materializes because of the marriage itself.
If someone told your friend or family member that marrying an inmate unlocks a government payment, that information is inaccurate. Anyone making decisions about marriage based on that premise is operating on a false premise.