Well, from another perspective, become King's concubine might be better than sold off to the brothel. She doesn't have lingering feelings towards her scum lil bro either. Even if she isn't favored, at least she will still get food and shelter. The most dangerous scenario probably favored and bore a crown prince but judging by the current royal family I don't think that would happen.
It's the princess who naive and at dangerous place. Assuming the person she run off with is trustworthy, can she survived commoner lives? If the person she run off with is not trustworthy, can she still survived?