Depending on family size in CT, one could have a full time (lower paying) job and still received medicaid. There are/were different levels, some that the recipients would pay into.
When I was in high school, every once in a while the grandkids would have to get 'gifted' a modest amount of money. This had to do with with how much money was 'in danger' of being carried over in the bank due to the timing of the payouts of their social security and his work pension. Too much of a balance could apparently cause an issue with their Medicaid eligibility.
A couple people in their late 80's, of very limited function, on the verge of getting tossed because they had an extra thousand bucks in the bank. Weird.