Does the hadith "Pray for your companion" apply to the utterly destitute person whose money was stolen and who cannot repay his debt, or to the chronically ill person who is unable to repay despite his efforts, or does it apply only to the one who is able to repay but does not? And do these individuals fall under Allah's saying, "Allah does not burden a soul beyond its capacity"?

Debt is not a barrier to praying over the deceased; rather, it is obligatory to pray over them. The Prophet's (peace be upon him) abstention from praying over a debtor was a deterrent against procrastination and negligence in repayment, and a warning against debt. It was said that this was abrogated by the Hadith: "I am more worthy of the believers than their own selves, so whoever among the Muslims dies leaving a debt, its repayment is upon me." Finally, the examples mentioned in the question (taking money with the intention of repayment or destruction) are not included in the warning found in the Hadiths.