Is it permissible for a woman who is ritually pure from menstruation to perform tayammum instead of ghusl due to illness?

It is not permissible to switch to purification with tayammum (definition) unless water purification is impossible, either due to the absence of water or the inability to use it due to an illness that affects the person if water is used. So, if a woman is ill to the extent that bathing increases her illness or delays her recovery, there is no harm in her performing tayammum.