I am getting conflicting answers from a lot of different sources. Most everything suggests that if you do not renew your contract, your Production Licenses will not expire and will still work, BUT you will not be able to update your version of Nintex Workflow / Forms from that point on. 

Additionally your Development Licenses will expire, and will render all of the Workflows and Forms unusable in any way. 

I think that this is correct based on my own On Premise environment which shows an expiration date on my development license, but not on my Production License. 

Sources That Agree with the above: https://community.nintex.com/t5/Blog/Nintex-Licensing-Frequently-Asked-Questions/ba-p/77113

http://nintexdownload.com/Nsupport/Nintex_Annuity_Renewals.pdf

Source that Disagrees with the above: https://community.nintex.com/t5/Best-Practices/What-happens-when-my-on-premise-license-expires-for-workflow-and/ta-p/90425

It should be noted however that changing servers means that you will need to acquire a new license as I believe they are issued per server. Additionally if you're migrating from On Prem to Online, that is a totally different product, so I'm not entirely sure you will be able to directly migrate your license from On Prem to Online without getting *some* sort of new contract.

(I'm not entirely sure that you can get a production license without a Software Assurance contract, honestly)

Your best bet to answer this would be to contact Nintex support directly or your Nintex Reseller who has invoiced you in the past.