Living in other EU countries while being on a work visa

Strictly speaking, you can't even work from another EU country for 90 days out of 180, unless your contract says so. Those days are meant for personal travel only. You are unlikely to get caught or have actual problems right away while working remotely, but getting into trouble someday is indeed possible.

For instance, if your employer gives you a faulty laptop, you get an electric shock and end up in a hospital, you will be entitled to the statutory work-related accident insurance. You will be paid while you are unable to work, and will receive free medical/rehabilitation treatment in order to be able to get back to work.

If the accident happens in another country, you will not receive the same compensation / treatment, or may have to pay out of the pocket for some of it. Your employer may also be fined for not paying insurance fees in the country where you actually worked, and if they didn't authorize you to work abroad, they may try to get that money back by suing you for damages. Finally, you may be fined by one of the countries involved (or both) for non-compliance with immigration policies and have your work permit revoked.

Even if there is no accident, if your employer finds out you're abroad while working for them, this will very likely be considered a violation of company policy or your contract, because your behavior creates potential legal trouble. You will be reprimanded, or, if you do it repeatedly, fired for cause.