No, taking welfare or unemployment does not mean one is not worthy of citizenship, nor does it mean one is merely voting to take others' stuff.
The vast majority of my graduating class is unemployed. I don't know if you all noticed, but some of us are stuck in a depression, on an arguably national and definitively local and industry-specific level. Most work and have worked a whole lot for free. Most perform a whole lot of charity. Most have paid taxes in the past and will pay taxes in the future. Many, perhaps most, are receiving some form of welfare.
I understand that most of us here don't agree with the way the system is set up. Determining that anyone who engages with the system in a manner appropriate to its current structure is somehow a lesser person than you is foolish.
Heck, why not go all Soviet--let anyone vote, as long as they only vote for proper American, y'know, one who agrees with you.
As for my thoughts on property ownership as a measure of a person's value to the American polity, see the other thread. To sum up: nuh-uh.