If one necessarily has to live in an apartment in order to be able to perform work for a company (e.g. relocation to a big city in Europe), would it one save money (in taxes, etc.) if the company reduced one's salary by the monthly cost of paying the living arrangements, and then the company would pay those living arrangements on one's behalf. Doing this should result in a lower gross income, and therefore less taxes?
For example, suppose company X pays $5,000 a month in salary and apartment rent is $1,000 a month. Would it be more financially sound to instead have company X pay a salary of $4,000 a month with the added benefit that company X now pays for the rent of $1,000 a month?
EDIT: To help out if relevant tax laws do matter, I am a U.S. citizen who would be working and living in Ukraine for a period of a year.