Depreciation exceeds income, do i get a refund?

[Charles Cruse]

Hi All,

Looking for some sources or answer if available. I am currently working abroad long-term. So I am not taxed in the US on the income I earn from my job. However, I do own a rental property in the US. 

I know I will have a taxable income from the rent I earn, but what if my deductibles from appreciation and expenses exceeds my earned income? Am I leaving money on the table here or would I receive a refund that accounts for this? 

I am considering investing in REITs since their dividends are taxed at ordinary income, but I’m also unsure if that amount can actually be affected by deductibles.

Any information is appreciated. 
Thanks!