I am well aware of coins with controlled inflation like BTC, where a finite number of coins will be generated at a controlled rate. Very recently I came across deflationary tokens where coins are destroyed whenever a transaction is made and they will end at some time.
My question is what is the purpose of creating such coins? Are they worthy enough to be invested ?
Every project created with a purpose, so if you want to know exactly about the purpose of a coin, you should learn it on their website and whitepaper.
Are they worthy enough to be invested? I don't know what kind of coin that do you mean, but the first thing about the investment you should learn it by yourself, if you think untrustworthy, so skip it