If someone has thin hair that easily comes out are they allowed to put their hair in a ponytail or remove the ponytail if the intention is not to take out any hair?
I am extracting several answers from this article that may be relevant:
May one use a ponytail holder to make a ponytail in her hair on Shabbat?
Making a ponytail and using a ponytail holder is permitted on Shabbat, as this is unlikely to cause the removal of hair (Yalkut Yosef, 303:15).
So, in general, you can make a ponytail. However, since you stated that it is quite likely that your hair may fall out,
May one stroke his beard on Shabbat?
Strictly speaking, it is permissible to stroke one’s beard on Shabbat, despite the possibility of hairs being detached, because the person neither intends to remove hair nor has any interest in doing so, and this outcome is not guaranteed to occur. Nevertheless, Hacham Ovadia Yosef (in Yalkut Yosef) rules that it is preferable to avoid stroking one’s beard on Shabbat.
So, it is really based mainly on the intent, and since you have no intent to remove your hair, there is a leniency.