The John Gardner I am interested in was born in Torphichan. I would imagine that he would have been a charge on that parish if a need had arisen?
Either on the parish of his birth or the parish where he most recently acquired 'settlement', which in his case would have meant that he resided there continuously five years. If he was in Slamannan in both 1851 and 1861, he would almost certainly have acquired 'settlement' in Slamannan.
However that does not mean that he would not have been dealt with somewhere else initially.
Suppose he had moved to Glasgow and shortly afterwards (i.e. not long enough to acquire 'settlement' in Glasgow) become ill or fallen on hard times. He (or someone on his behalf) would have applied to the Glasgow parochial board for 'relief'. The Glasgow Inspector of Poor would have visited him and gathered all relevant information, including his parish(es) of birth and settlement, names of wife and children, ages of children, and the circumstances leading to the application. The Inspector could give temporary relief, which could include sending him to the poorhouse in Govan, and then reported to his Board.
The Glasgow parochial board would then write to the parochial board in his parish of settlement to notify it that one of its paupers was being supported, and to ask that Board to decide how to deal further with him. The other Board could either ask Glasgow to keep him in their poorhouse and agree to pay his costs there, or ask them to send him to their own poorhouse or other appropriate place.
So if I were you I would be falling over myself to see the Glasgow parochial board's records of John Gardner. They should be in the City of Glasgow Archives in the Mitchell Library.
(PS different procedures apply before 1845; until then, paupers were dealt with by the kirk.)