Here are case examples of churches giving to the poor, which may prove a useful reassurance to your question of "why does this not happen nowadays?"
I was a member of a Lutheran congregation that had a budget commitment for "Benevolence" (which was everything from running the national denomination's HQ to missionaries to Lutheran Social Services). The congregation also gave another 10% of its budget to "Social Ministry", which was distributed to a number of local and national direct-relief charities for the poor. That congregation also had budgeted a few hundred a year for a pastor's discretionary fund, mostly people for people in trouble who'd stop by the office ("I ran out of gas", etc.).
At the same time, both that Lutheran congregation and my current one (a non-denominational evangelical one) have regularly held special offerings for a member of the congregation in trouble. Usually a medical emergency that devastated the family's finances.
As far as whether Christians should "give up all they have", that passage is about challenging one's faith: is it in your own works? There are two passages that should be thought about in relation to each other.
But Zacchaeus stood up and said to the Lord, "Look, Lord! Here and now I give half of my possessions to the poor, and if I have cheated anybody out of anything, I will pay back four times the amount."
Jesus said to him, “If you want to be perfect, go, sell what you have and give to the poor, and you will have treasure in heaven; and come, follow Me.”
In the first case, Zaccheus tells Jesus that as an act of contrition, he's voluntarily giving half to the poor, and is commended by Jesus. In the second, the rich young ruler first lies to Jesus by claiming he has kept God's law since his youth. Confident that his level of obedience has justified himself (has earned salvation), is told that the requirement is to give all to the poor. Jesus forces the ruler into a situation where he has to either go away or seek out some other source of righteousness (i.e., a source which comes from faith in Christ). Other passages tell us to give to the poor (Deut 15:10-11) and to him that asks of you (Matt 5:42). These are literal commands of Jesus: obey them, whether the person has short term need or is destitute. Today, we would remind anyone confident that their level of economic fairness or social justice has earned favor with God that the requirement is to give all (Matt 5:42). To the one in despair over their sins, they are reminded of God's free, unearned grace to those who believe.