Most licenses never expire, but software maintenance expires. The Home version is always a "perpetual license"; any Professional license you purchased individually is very likely a "perpetual license"; Student Version licenses are typically "perpetual license". Trial licenses are, though, "term licenses".
However, there are some Student Version licenses that are only good for 8 months or 1 year, and there are Student Version licenses issued for online courses that are only good during the course.
Also, some large organizations license for limited times, as it can be easier to get funding for a "service" than for an "purchase".
When a "perpetual" license expires, you might lose access to some mathworks.com documentation for older versions; you would continue to be able to access your own version's documentation from within the program.
When a "perpetual" license expires, you will still be able to download the last version covered by your maintenance contract, and all earlier versions, but you will not be able to download newer versions.
When a "perpetual" license expires, you will no longer be able to create new technical support cases, except ones involving installation and licensing.
When a "term" license expires, the software can no longer be used. However, if you created an executable using MATLAB Compiler, it will continue to be usable, with the exception that executables created using Trial licenses will expire as well.
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