No one can be jailed just for owing a debt, or failing to make payments on a contract. You can, however, be criminally charged and, if convicted, jailed, if you act to deprive an owner of their lawful property. I haven't seen this 'rental agreement,' but my best guess is that you're obligated to return the property you borrowed if you can't make the payments. The potential criminal charge lies in holding onto the rental property (whatever it is) while knowing that you have no right to it. Whether this is a felony or lesser charge will depend on the value of the property.
The point is, you have to return these items, or criminal charges may follow. Once the property is back in its owners' hands, though, then you are in no further danger of criminal liability for any debt that you might owe them. Any debt collector who tells you that you can be jailed for failing to pay is acting in violation of the Fair Debt Collections Practices Act, and can be sued for up to $1,000 per violation. (Don't get your hopes up on this score, though. The amount of the debt is usually higher, and violations of the Act don't actually erase the underlying debt.)
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I would question whether you can be guilty of, or charged with, theft, merely because you fail to perform any obligation under the contract (assuming you came into possession lawfully), although I can see there might be an argument to that effect. An attorney would have to see the contract.
If the company is threatening criminal prosecution in order to collect a debt, and if the circumstances are such that no prosecution is possible, that might be a violation of fair debt collection laws.
As a practical matter, however, you may want to consider whether it's worth while going through the hassle to hold on to the item if you can't pay.
This comment is general in nature and is not intended as legal advice. It does not create an attorney client relationship and obviously is not confidential. You should contact an attorney in your area who can review with you all of the relevant facts and give you specific legal advice.