This might happen temporarily every few months or so, generally for technical reasons or something that needs our attention more in real life.
When possible, there will be a notice posted in advance to give people a chance to get their applications in before a closure. When we close applications for any length of time, that just means that the process of accepting new members is on hold. All applications received before it closes will be processed as usual. The time period may or may not be specified, depending upon the reason.
Also, there are still existing members somewhere in The Spiral whether the application is open or not.