I have a family member in eagle pass jail I'm maverick cogcounty and I was wondering how to check if he qualifies for paroll or what his current status is.

That begins and ends with the sentencing judge. Parole is a privilege that can only be offered by the judge in the Judgement and Commitment document. This will detail all the elements of the crime, the sentence and all stipulations attached - call the clerk of the court and ask for the judge's secretary, they have the information and it is available to the public for the asking.