Dilaudid is safe as long as it is taken as prescribed by her doctor.  Dilaudid is the brand name for hydromorphone, an opioid (narcotic) pain reliever.  After your mother has taken Dilaudid for awhile, if she should want to discontinue it, she would need to consult with her doctor and gradually taper off of it to avoid withdrawal symptoms. 

Here's more information about Dilaudid:  http://www.healthcentral.com/chronic-pain/find-drug-25182-25.html

Often family members are concerned when they're loved ones need to take opioid medications for pain because they fear they may become addicted.  While they will develop a physical dependence on the medication, that is very different from addiction.  It is rare that a pain patient becomes addicted.  If you have any concerns in that area, I'd encourage you to read:  Opioids:  Addiction vs. Dependence