Is a PIN reducing the security of a fingerprint based encryption? Many smartphones and programs are using fingerprint's to secure the phone or encrypt data. In many cases, those programs want a PIN as backup authentification method.

A PIN just got 10000 possible combinations, while a fingerprint got many more. So an encryption isn't safe if there is a backup pin, is it?

The same question for a phone lock-screen: If there's a 4-digit PIN, people could just bruteforce this pin instead of bruteforcing million of fingerprints, couldn't they?
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A backup plan is always necessary in case the fingerprint sensor doesn't recognize fingerprints or gets broken or something that it doesn't function as expected 
Coming to app locking system, it totally depends on the app lock system if it has limit of trying PINS then you should be safe but if it doesn't YES it can be bruteforced if there's no limit on no. of wrong attempts 
Coming to Androids PIN lock feature, it doesn't have limit of only 4 digit PINS so you can make it more secure by making large complex PIN 
Assuming 4 digit PIN, AFAIK Android wouldn't allow you to attempt 10000 wrong PINS infact it will allow only few and then will lock up itself