If you quit you must quit for good cause assoicated with the work or medical reasons. If she is terminated for reasons other than work related misconduct she can recieve benefits but there are many variables. Here is info from the texas workforce commission website.

You must be unemployed or partially unemployed through no fault of your own to receive benefits. Examples of qualifying reasons are:

• You were laid off due to lack of work.
• You are still working but the employer reduced your hours. (Your reduction in hours must not be the result of a disciplinary action.)
• You were fired without work-related misconduct. Examples of misconduct are: a violation of company policy; violation of law; neglect or mismanagement of your position; or failure to perform your work acceptably if you are capable of doing so.
• You quit your job for a good work-related or medical reason. TWC may rule good cause if the work situation would cause a person who truly wants to keep the job to leave it. Examples of possible good cause are: unsafe working conditions; significant changes in hiring agreement; or not receiving payment for your work. You should also have tried to correct the problem before quitting. Examples of medical reasons are: quitting on your doctor's advice, or quitting to care for a minor child if required for a documented medical reason.
• You quit to protect yourself from family violence or stalking, evidenced by an active or recently issued protective order, a police record documenting family violence or stalking directed against you, and medical documentation of family violence against you.

If you quit to move with your husband or wife, you may be able to receive benefits after a disqualification of 6 to 25 weeks. This is a disqualification of both time and money, because we must subtract the number of disqualified weeks from your total benefits.

I was a hearing officer for TWC for 2 years (2002-2004) and all decisions are made based on past precedent. This link lets you look at the appeals manual and see what guidelines hearing officers have to follow when determining if a person is eligible for benefits. http://www.twc.state.tx.us/ui/appl/app_manual.html

In my expierence, if you get written warning for misconduct you must prove that you did not do what the write up claims you did. So if she did not fill a clients order but was out WITH PROPER NOTICE for medical reasons she did not commit misconduct so if they fire her she would be eligilbe. Don't be too concerned about a firing on your history (as long as it is not a pattern) you can explain the situation to potential employers so that they will not use it in a negative way.

If she quits under the current set of facts she will not be illegible for benefits. She must tell the employer she has a complaint and allow them to remedy the situation. If they continue to discriminate against her for being out WITH PROPER NOTICE then she could leave with good cause associated with the work.