No – that only applies to someone who is not liable. The JT’s will be jointly and severally liable.
What you can do is to apportion the rent between the JT’s as appropriate (even for CT’s). You may deem 100% to 0% as reasonable in the short-term for instance. See part of reg 12 below – note its the “rent paid” and not liable to pay that you have to consider. “All the circumstances” would surely include taking into account one of the liable persons going to prison.
“Where more than one person is liable to make payments in respect of a dwelling, the payments specified in regulation 12(1) shall be apportioned for the purpose of calculating the eligible rent for each such person having regard to all the circumstances, in particular, the number of such persons and the proportion of rent paid by each such person”.