There are certain missions in RDR 2 that requires you to give away money to complete them, such as "Do Not Seek Absolution II" and others. But what happens in these missions if your bank account is empty and Arthur does not have any money to give?
You have good friends. Even if you are without money on missions that require it you will find prices are lower than they would normally be, there's a cheaper version of the necessary item, you can choose an alternate course of action, or friends will give you cash.
Minor spoilers below for three Chapter 2 missions, but nothing too far into the game's storyline.
For instance, one of the earliest missions in the game A Quiet Time culminates in you running from the police while thoroughly inebriated. If you are caught you won't have to pay the $10 bounty because your buddy pays it off for you.
Two missions later you're invited to shop for horses in Exit Pursued by a Bruised ego. You are obligated to sell off a horse and purchase a new one with the money. There are three options available: A Morgan horse for $15, an American Standardbred for $150, or a Dutch Warmblood for $450. If you are (unsurprisingly) unable to afford the $450 horse, and the moderately expensive $150 horse. You may notice that the sale price of the draft horse you sold ($5) will not be enough to allow you to purchase the cheap $15 Morgan.
If you are so insolvent you cannot supply the other $10 to afford the $15 horse you will have to reload the save and instead choose to stable the draft horse rather than sell it.
Lastly, in one of the mission The Sheep and The Goats you will need to purchase a Rolling Block Rifle - an expensive weapon typically selling for $189! Thankfully your buddy John Marston will call in a favor and have the gunsmith sell it for free, thereby saving your wallet and ensuring you can purchase the firearm.
There are a variety of ways to continue a mission even if you don't have the requisite cash. In most cases it will not require reloading a mission's checkpoint, but it is not impossible to force that hand either. No matter what, the game will make accommodations for Arthur Morgan.