Paul writes about generosity in this chapter. Paul says that if you give to those who are undeserving, you are displaying the grace of God poured out on you. We are undeserving of God's grace, but He bestows His grace upon us regardless.
Sometimes, we look at our finances, and think- boy, we don't have any left to give. Giving should be sacrificial. The church Paul is talking about gave "in a wealth of generosity" when they were going through a major hardship and extreme poverty. They gave even though they themselves were suffering financially. Paul was also surprised at their giving because they first tithed to God, then after, they gave to Paul and his co-ministers to provide for their needs. Paul says in verse 3 that they, gave according to their means, and beyond- on their own accord. This means, they gave because they wanted to, not because they were obligated to.
Poor and rich in this verse do to refer to monetary status. Jesus, who was in heaven, came down from earth in humility, and experienced life and death on earth (poor), so that we might come to know Him and be filled with all the blessings of salvation and relationship with Him (rich).
Paul is not telling you to give money to someone if it provides for them but leaves you struggling. He is just suggesting that when you have more than you need, to help your fellow believers who are in need.
When we realize that all things come from the providing God, we also recognize that all the money we have is not really ours to begin with. When we come to the place in our hearts and minds that all that we have is not ours but God's, what we are given by Him- we can give generously and joyfully.
For you know the grace of Lord Jesus Christ, that though he was rich, yet for your sake became poor, so that you by his poverty might become rich.