Taking over a no longer maintained or supported plugin

I’ve been using the SABRE plugin on one of my websites for many years. Although it’s not been updated in more than 3 years it still works perfectly. I was recently asked to put it into another WordPress website and it failed to activate (I’m guessing changes to WordPress or PHP version). As it’s such a useful plugin my question is

Can I take over the development of it? Either the current plugin, or copy and fix the code for a new plugin?

If so – which and what do I need to do.

Many thanks

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