Twitch poisoned subs?

If you get a sub poisoned on Twitch, do you automatically pay for a new one after the 30 days have expired?

No. If you get a sub for free and do nothing, the sub will not be automatically renewed after it expires.

Only if you actively renewed the gift sub would it become a paid subscription, which would then extend until you cancel it.

In…
https://www.twitch.tv/...scriptions" class="text-primary">https://www.twitch.tv/...scriptions
… You can always see the status of the current subs and change them if necessary. You can also see if and when a sub is extended. Respectively. Here is the tab for the free subs…
https://www.twitch.tv/subscriptions? Tab = gifts