That did happen once, after the college of cardinals was deadlocked for two and a half years. Every once in a while they would take a ballot, and cardinals who wished to abstain took to writing in “Peter the Hermit”, a saintly old man who lived up a mountain and sometimes answered letters that were sent up to him asking for advice. Finally, to their horror, they counted the ballots one time and found that Peter the Hermit had gotten a majority. They sent him an apologetic letter, “The Holy Spirit, which like the wind blows whichever way it wishes, has moved us to elect thee Supreme Pontiff.” He did not want the job, but the king of Naples, who had been a generous sponsor of his favored charities, promised to help with the administrative tasks. This “help” turned out, of course, to consist of selling valuable church positions to the highest bidder. Once the Hermit Pope, formally named “Celestine V”, figured out how crooked everything was, he resigned-- this is one of only two times that an undisputed Pope has resigned before now.
The cardinals had learned their lesson and elected a cynical financial administrator from the bureaucracy as Boniface VIII. Within months, the ex-Pope Celestine was found murdered, and suspicion latched on to the new Pope’s cardinal-nephew (nepotism was routine; it was considered standard practice to give one young relative the “red hat” so that there would be at least one person in the college of cardinals the Pope could trust; some cardinal-nephews were well respected, but this one was a rogue). Boniface subsequently was arrested by the king of France, supposedly on charges of atheism and the murder of his predecessor, but really for not letting France tax the churches. This resulted in the move of the Papacy to France, and ultimately the Great Schism when there were two Papacies, in Rome and in Avignon, and then for a while three, with a compromise Pope in Pisa who got no traction.
Other resignation cases have involved disputes over who was the rightful Pope, one of the claimants finally giving up and agreeing “OK, I’m the Antipope and you’re the Pope”. At the end of the Great Schism, the Pope in Rome resigned while the Avignon and Pisa Popes had to be forcibly ejected, so retroactively he is counted as “rightful” Pope-- and this is the source of the factoid that “1415 is the last time a Pope resigned”. The last time a disputed Pope gave up was 1439 (antipope Felix V had the loyalty of several churches in Savoy, Switzerland, and Bohemia, last antipope to have a substantial faction); the last time an undisputed Pope resigned was 1296 (Celestine V) and the only other time that has happened was Benedict IX, an even more unfortunate precedent than Celestine.
He was a teenager put on the papal throne hastily (ordained priest, consecrated a bishop, raised to the rank of cardinal, and elected Pope all in one day) as a puppet of his family, and interested in the title only because it helped him to pick up chicks; his favorite mistress took to calling herself Regina “queen” of Rome. Even by 11th century standards this was considered unseemly, so he was pressured to resign, but he did so by auctioning off the Papacy to the highest bidder. Although the fellow who bought the Papacy was sincere about wanting to redeem the church from its dominance by local corrupt political families, his excuse that he had bought the position to prevent it falling into worse hands was not accepted and he was driven out of the city. Benedict came back, and was Pope again for a while until he was pressured to resign again. During subsequent fights over who would now be Pope he managed to take control of Rome briefly for a third time, though only to grab some hidden stashes of money and disappear. One version has it that he was captured and quietly confined in a monastery somewhere, but I like to hope that he and Regina made a clean get-away.