Translation:I was sleeping at my parents' for a week.
When I see "przez", I imagine it as a period of time with a defined beginning and end. Thus, I would say it can only mean that she is no longer staying there. It could be a long time ago or she might be just moving out, but she is no longer going to.
If she was still going to sleep here, but only wanted to mention how long she already has, she would say "Od tygodnia śpię" (note the present tense).
If she is in the middle of her stay, but she knows it is going to be a week in total (for example, she has already slept 4 nights and will stay for 3 more), she would say "Przez tydzień śpię" (again, the present tense). Similarly, if she has plans to stay for a week some time in the future, she would say "Przez tydzień będę spać".
I think it may be translated as both of those, depending on the context...
I found this https://britit.blog.polityka.pl/2017/09/11/top-5-grammar-problems-for-polish-learners/, see the first problem.