Example input

OOOOOOOOOO
O    O   O
O OO O O O
O  O O O O
O OO   O  
O OOOOOOOO
O        O
OOOOOOOOOO

Starting point: (x=3, y=1)

OOOOOOOOOO
O    O   O
O OO O O O
O• O O O O
O OO   O  
O OOOOOOOO
O        O
OOOOOOOOOO

Desired output:

OOOOOOOOOO
O••••O•••O
O•OO•O•O•O
O• O•O•O•O
O OO•••O••
O OOOOOOOO
O        O
OOOOOOOOOO

Notes

As the problem has some open questions, I assumed the solution should accept multiple types of mazes (including ones with cycles). Therefore, I've chosen to implement the solution using BSF with backtracking.

I also focused on the correctness of the algorithm first, and decided to test multiple error cases (e.g. invalid starting position, invalid maze, invalid size) later. Should I have more time, I'd test those cases.

Additionally, if I knew the nature of clients of this application (API), I could consider different encoding of the HTTP messages. Most likely, I would make the API RESTfull and JSON-speaking as that's what the clients would probably prefer.

I would also avoid using an exception in the case of no escape path. Such a maze should be considered correct (e.g. Minotaur's Labirynth), therefore the application should not use exceptions to handle this case.