Question on Discretionary leave to remain refusal

[lsu]

My parents came to the UK to visit my family and unfortunately my father passed away during the visit in the UK. My mother then suffered depression, and applied for Discretionary leave to remain. Her application was refused.

She is allowed to submit an appeal within 14 days.

The question is: If she does not appeal and returns back to her home country, I wonder if she is still eligible to apply for visitor visa? How good the chances are for her to get visitor visa in the future?

Thank you for your time and help on this in advance!