How to check penalized or banned websites?

If we search the website from its name without www. or extension like .com and it appears in search then we can say it not penalized nor banned and if it doest not appear in search result then it may be penalized or banned.

When Google penalizes a website, they will decrease your site's visibility by bumping your organic ranking down in the search engine results.  Google has different levels of penalties based on the severity of what they feel is "unethical" or "malicious" SEO practices.

First of all check in webmaster tool is there any manual action has been occur or traffic decline.
or else go to feinternational.com/website-penalty-indicator 

Normally I will check it on Ahref to see whether it still works or not, or its current traffic rate throughout recent months or even years. If it has tremendously low traffic rate then high chance that the site was broken.

There are many tools to check google penalty:

pixelgroove.com/serp/sandbox_checker/
https://feinternational.com/website-penalty-indicator/
https://fruition.net/google-penalty-checker-tool/

You can find the website issues in webmaster tool. It is best pa=lace to check as well as to recover website to normal.

If we search the website from its name without www. or extension like .in and it appears in search then we can say it not penalized nor banned and if it does not appear in search result then it may be penalized or banned.