You are hoping to pay "whatever you can" to the creditor since you can't afford the minimum, but you want to send in something to keep in good standing. This strategy may work for a few months, but not forever. You will be assessed a late fee each time you don't send in the full minimum payment. The creditor's computer system eventually will notice the underpayment and will send the account to its collection department.
At some point, the creditor will charge off the account and one of three things will happen: The creditor will sue you, assign the account to a third party collection agency that will try to collect on the account, or charge off the account and have an independent collection agency try to collect on the account.
Unless the creditor or collection company accepts the monthly payment you are offering, you may eventually be sued. Creditors do not sue on every single account, but it is possible that either the original creditor or a collection agency will sue you to collect on the account.
You are not likely to be arrested for failing to pay on the debt, but you could be arrested for failing to respond to a court order resulting from any lawsuit. Throughout the lawsuit process, the judge may order you to appear in court and explain why you are not paying on the debt. There may be numerous names for this request throughout the country, but in general, it is called an order to appear for a debtor examination.
It's a court order for you to explain why you are not paying on the account. The judge may issue a bench warrant for your arrest if you fail to appear at this hearing. The local sheriff department may actually come to your residence to arrest you.
I have only heard of this happening once and a huge percentage of my clients have been sued. I just don't know how aggressive the sheriff department is in every single county throughout the United States. It is more likely that you will get into trouble if you get pulled over for a routine traffic stop and the warrant shows up in the computer.
I am not writing this to scare you. I hope it actually has the opposite effect. While it is serious when you are sued, you are not likely to spend time in jail for failing to pay your credit card debt. It is more likely that you will have your wages garnished or bank account levied. After all, the creditor can't make you pay when you are in prison since it is hard to earn a living behind bars.