I have a streak that just passed 500. If a responsible official asked me to self-quarantine due to the covid-19 pandemic, I would be disappointed but I would certainly voluntarily halt the streak. It would feel better to stop it when it the decision is partially up to me. At least that's how I look at it, given the way that this question is framed.
If or when I contract covid-19, that decision will be out of my hands... and of course a streak would be the very least of concerns then.
Having said that, no part of my country has taken the extraordinary step of mandating quarantine for this pandemic. Even a shelter-in-place order allows for going outside, which is what geocaching is all about. Moreover, I am fortunate that in my somewhat rural area it is possible to target many caches that have not been visited in weeks or months or more, and are probably not going to be visited by someone else in the very near future.
Primary concern with covid-19 is person to person transmission. I'm following sanitation guidelines before and after caching but if I keep my distance from people during my outings, according to available info that's the best thing I can do. And that's what I will continue to do.
Be well, everyone.