As I understand it, Roman tax collectors would pledge to collect a certain amount of taxation, and could keep whatever they collected above that amount. What sort of consequences would they face if they couldn't deliver the amount they'd pledged?

Now, I cannot speak to the Roman system specifically and, presumably, the Roman system itself changed widely over the many years of Republic and Empire. But the general concept you're talking about is common and was known as taxing farming (Wikipedia link). It really survives, in places, from the birth of coordinated empires right up to the modern period. It was eliminated in England in the 17th century in favor of a centralized tax collection system, but it existed even in France right up until the Revolution, and in most of the rest of Europe and the Middle East well into the 19th century.

Instead of thinking of it as pledge to give a certain amount, you can think of it as a right that is sold. Sometimes this was auctioned off but, as with many of rights in aristocratic systems, these often became de facto and in some case de jure inherited rights within certain families--again, though, we're talking widespread variations throughout history. What happened when someone couldn't pay would vary, but depending on the details of the system, it was often just sold to someone else who would then just be more cruel in their tax collecting than the last guy.

Why have such a system in the first place? The state's revenues often depends on control and information. I have an older posts going into that here, but here's a sweet table from Charles Tilly that, in a way, sums up a lot of his argument. On the X-axis you have monetization, that is, how much money you get through each form of extraction, and on the Y-axis you have surveillance, that is, how much does the state have to know to harness that mode of extraction. As you see, the two are correlated: the more money you can make from something, the more the state needs to know (the more developed the state has to be) to get it. Tribute is the simplest form: you basically need to know nothing. "I have big rock, you give me big money." Rents on state land, especially for agriculture, require just sending people out once a year during harvest time to collect--this was often a hated local tax farmer, who had extensive local knowledge. Taxes on stocks (like land) requires more information, which is why we get big land surveys like cadastres before we get big population surveys like censuses. Flows (duties, tolls, etc) requires more knowledge (control of key chokepoints), and so on and so on until you get to income tax, which requires you know a lot of things about basically everyone for it to work. A VAT tax, popular in Europe, requires a tremendous amount of information but to paraphrase one economist whose name I’m blanking on is a “money making machine” but requires the state to keep track of almost every single transaction (which is why it’s been so doubly rejected by many who wish to shrink the state)

These sorts of rents and stocks (here, often stocks of land, so property taxes) require the least next amount of information. But even this information was often hard for the central state to have and often requires very local knowledge. Things like cadastral surveys, in most places, tend to appear much later than you might think. This meant that it often made the most sense to sell this to someone who might have or be willing to acquire local knowledge, rather than developing a permanent bureaucracy who might end up skimming off the top anyway (who will watch the watchmen and all of that).

Tax farming, rather than a tax on a stock like a property tax, is really a form of a rent that is sold off. Just like you might rent a house for a year, you may rent the right to collect all the various taxes in a given area for the year (or maybe you just rent the right to collect one kind of tax). Like other rents, what does the owner (here, the state) do when someone cannot pay rent? They end your contract with renter, and rent it to someone who can pay. In the tax farming systems that I am familiar with, especially in the Ottoman Empire (who took much of the tax system from the Byzantines, who were really just very late Romans), those who rented the right to tax farm were wealthy families who had the money to pay. It might then be subcontracted, even. In general, wherever it occurred, the system was widely abused and therefore profitable for the tax farmer, who would do everything from undervaluing the goods collected (taxes were often collected in kind, so the tax farmer might be responsible for turning these goods into cash) to charging taxes on things they had no right to change taxes on or at rates that exceeded what they were legally allowed to. Again, the Roman Republic and Empire are not my area of expertise, but I am unaware in the Ottoman Empire or in pre-Revolutionary France of a tax farmer not being able to pay their pledge. Their may have been cases, but it certainly was not a common thing. Much more common was for these rich families to become considerably richer on the backs of the peasants.