The question is emminently worthy of discussion.
We might still not like the answer. The answer is not simply yes or no, it is more like a restatement of the question such that we ask, under what circumstances might a nation not have an obligation to provide that level of support?
We can imagine material situations under which providing such support might simply put others into the same deplorable position... there simply is not enough to go round. This does not apply here and now, but recognizing that this is a possible reason for not doing it allows one to then check off, this does not apply here.
Conservative thinking would ask that it be evident that the poor show that at least such things as the individual could do for themself are being done, somewhat as a good for the soul point of view. The approach also has the benefit that case 1 would be less likely to occur.
Generally we do want people to try to carry their own baggage if they can. Well, what then do we do about the individual or family without the will to try when we perceive them to be able?
Do we assume that they are emotionally crippled and so treat them as sick, unable to try? Unless case 1 applies, we probably do. We try as loving neighbours and friends to coax them to try, but we do not leave them homeless or hungry, we clothe them respectably so that they do not face an insurmountable barrier to getting work etc.
They are part of a family that has adequate income that is being squandered or hoarded by one person in the family... do we go on increasing the money this controlling person is wasting or hoarding? Do we force disollution of the family unit so that they can be helped separately?
The family is trying to farm. Is anything further needed to describe this idiocy? How can we help a farm family when every cent gets plowed down with the farm debt?