"Paso'ach Tiftach Es Yadecha Lo", open up your hand to the poor (Re'eh 15:8). The Gemara in Bava Basra (10a) tells the story how Rav Papa was walking up the stairs and his foot slipped and he was about to fall. Chiya Bar Rav MiDifti said to him, "Maybe a poor person came to you and you did not support him." What is the connection between an accident on the steps and not giving tzedaka?
I am a bit hesitant to give this answer, it seems speculative, so take it with a grain of salt.
The Marsha connects the above mentioned Gemara to a previous Gemara in Baba Basra Daf 9a. The Gemara says as follows: "A Tanna taught: If he is a beggar who goes from door to door, we pay no attention to him. A certain man who used to beg from door to door came to R. Papa [for money], but he refused him. Said R. Samma the son of R. Yeba to R. Papa: If you do not pay attention to him, no one else will pay attention to him; is he then to die of hunger? But, [replied R. Papa,] has it not been taught, If he is a beggar who goes from door to door, we pay no attention to him? — He replied: We do not listen to his request for a large gift, but we do listen to his request for a small gift. (Soncino Transalation)
Perhaps the incident of Rav Papa almost falling from the ladder indicates that Rav Papa had not placed his footing properly. He had not anticipated the consequence of how he placed his foot could lead to his fall. Similarly Rav Papa did not anticipate the consequence of not providing the beggar money. His action although seemingly justified was a slippery slope that would cause others to imitate thus causing the death of the beggar. Sometimes an act alone could be justified, but if everyone acted that way it would bring about a terrible consequence.
I need to think about this some more, but this is a first stab at it.
He doesn't like the trop explanation because of how common darga-tevir is. Instead, he notes that the Midrash associates ladders with people's fortunes rising or falling, and suggests that the symbolism here is that R' Papa was climbing the wealth ladder but not being careful enough to help those who are lower on the ladder than himself.
The Vilna Gaon in Kol Eliyahu explains using the "Trop". That is the notes used when reading in the Torah. If you look at the words Paso'ach Tiftach in the Chumash you will find something of great intrigue. The Trop on these words are "Darga" and "Tevir" which in Aramaic means "Steps" and "Break". Now we understand why after seeing Rav Papa's accident on the stairs, Rav Chiya Bar Rav MiDifti's first thought was it had to be a tzedaka issue, as he had just experienced seeing someone on steps that were breaking. This explanation of "Darga" and "Tevir" can explain another interesting Gemara in Shabbos. Dovid asks Hashem "when will I die"? Hashem replies "I can not tell you" .He goes on and asks at least tell me on what day of the week? Hashem answers him" it will be on Shabbos". Dovid with the information in hand has a plan to extend his life. Being that I must die on Shabbos I will learn all of that day and render myself untouchable to the angel of death. Being that the power of Torah will protect me. When the day of his death came the angel of death had his own counter plan. He made the trees outside rustle to such an extent that Dovid was forced to see what was happening. Dovid went up on a ladder the rung broke and as a result he died. Here again we have the theme of falling from the ladder .The question is what is the connection?
The Gemara in Brachos gives Dovid's daily schedule and says everyday: כיון שעלה עמוד השחר נכנסו חכמי ישראל אצלו אמרו לו אדונינו המלך עמך ישראל צריכין פרנסה That is every day the wise men would come and tell Dovid the Jews need money he would say "let them do buisness with one another, and so they will earn their money" they further told him your system is not working so he said in that case capture the thieves and that will solve the problem. Reb Yonasan Eibshitz says this was a daily occurrence, he gave that answer on a daily basis and apparently it was not helping, Dovid was missing the point. The Jews needed Dovid to do or say something more practical .He brings down a Yalkut Shimoni based on a Posuk in Divrie Hayomim. There Dovid lists exorbitant amounts of money he had saved up to build the Beis Hamikdash. It further says when there was a three year famine in the land he refused to give up any of the money, as he was saving it for the Beis Hamikdash. The Yalkut brings down that this angered Hashem. Dovid had his priorities wrong because Hashem had said tzedakah is greater than the building of the Beis Hamikdash. Therefore he was punished by not being allowed to build the Beis Hamikdash. To add insult to injury the money was never used for the building of the Beis Hamikdash. As we know from Melachim that only after the completion of the Beis Hamikdash did Shlomo take out the money and put it away in the treasuries. That is because he was instructed by the Nevim of his day that this money was not to be used to build the Beis Hamikdash (Pesikta Rabbosi). Now we know why Dovid died with a fall from the ladder as he forgot the poor. Therefore he got the "Darga Tevir breaking step as his final death blow.