All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
As long as your sister came while intending to perform ‘Umrah, then she is not allowed to pass the Meeqaat without assuming the state of Ihraam.
The fact that she has menses does not prevent her from assuming the state of Ihraam for 'Umrah. However, it is allowed for her to remain in Jeddah until she becomes pure and then she can perform Ghusl (ritual bath) and go to perform 'Umrah.
If she had passed the Meeqaat without assuming the state of Ihraam, but can return to it and assume the state of Ihraam from the Meeqaat once she finishes her menses, then this is acceptable.
However, if she had assumed the state of Ihraam from Jeddah, then she is obliged to offer a sacrifice because of passing the Meeqaat without assuming the state of Ihraam.
Jeddah is not a place of Meeqaat for the one who comes to it from outside, according to the most preponderant opinion, such as someone who comes from Riyadh for example. However, the residents of Jeddah can assume their Ihraam for their ritual from Jeddah.
For more benefit, please refer to Fataawa 369067, 136830, 90293, 115836, 101583, and 15006.
Allah knows best.