(may Allah bless him and grant him peace):
“When I command you to do something, do as much of it as you can.”
This woman can fulfill all the requirements except this one. Prayer is more important than circumambulation, yet if someone cannot fulfill its conditions—ritual purification, covering the parts of the body that must be concealed, or facing the qiblah—he prays as his circumstances allow. This concession applies all the more to circumambulation.
If she were experiencing non-menstrual bleeding and could only circumambulate with the impurity of blood upon her, she would pray and circumambulate in that condition, by agreement of the Muslims, provided she performed ablution, cleansed herself, and did whatever she could. When a menstruating woman circumambulates, she should bathe and secure a cloth to contain the bleeding—that is, take protective measures—just as she does when entering ihrām.
The Prophet (may Allah bless him and grant him peace) waived the farewell circumambulation for menstruating women. He also waived the overnight stay at Minā for those responsible for supplying water and for herdsmen because of their need, and did not require them to make a sacrificial offering, since they had an excuse, unlike others.
Likewise, anyone unable to stone the pillars himself because of illness or a similar reason appoints someone to do so on his behalf and owes nothing further. Someone who omits an obligation because he is unable to fulfill it is not like someone who omits it for another reason. And Allah knows best.