No, you contract with another business to employ them on your behalf. Legal, common, and much more flexible.
mandatory legal benefits like generous sick and parental leave still apply
They are still cheaper despite all that...
not if they're in a different country, and if they're employed as contractors
>you contract with another business to employ them
That another business is liable to pay them
No, you set up your own legal entity(company) based on the financial/legal framework in your country, and bill your foreign employer for the work you do, but you're not an employee so you have no right to sick days, firing protection, etc. and have to do your own taxes.
Note that if the employer is found to be engaging in "disguised employment" then, in some jurisdictions such as the UK, they may be found liable for these things anyway plus penalties.
I know, some countries like UK, Germany, Austria, etc have laws to discourage this, but in Eastern Europe(Poland, Romania, Bulgaria, etc) this is totally legal.