In the US, there's typically COBRA as well so you can continue your previous insurance for up to about 18 months--without your previous employer co-pays of course.
It was quite a few years back but I don't remember it as being a big deal after I was briefly laid off post-9/11. As I recall I filled out forms to be covered but never actually paid in because there's a grace period and I got a new job after about a month. All things medical can get complicated, but COBRA should just be a continuation of your existing coverage.
If I want to avoid coverage loss, I'll go with back-to-back employment rather than risk a few days and having to enroll in COBRA.