Unfortunately, that is not how a democracy works. Neither a government entity nor an individual can remove a constitutional right of others due to the person at hand being in a "debtors prison" or by the whims of the state. Welfare is an aspect of having a government and having order and the fundamental of that is paying taxes. Although, originally only white men that owned property could vote. 

Remember that Alaska takes a third of its income from the Federal government..... The state you live in is on Welfare should it be barred from voting??