JetBrains has transfered its software into a subscription-based model. Is there any way to use JetBrains software without an active subscription?

Yes, there is a way to do that. When you purchase a yearly subscription from JetBrains, you will get a so called fallback license. This license entitles you to use the specific version of the software product which was available at the time of purchase without an active subscription.

Source: official JetBrains Licensing and Purchasing FAQ, retrieved 2016-11-17 (https://sales.jetbrains.com/hc/en-gb/articles/207240845-What-is-perpetual-fallback-license-)