Pawsitivity trains service dogs for people who are deaf and also for people with hearing processing disorders.
The #1 task that a service dog for the deaf is trained to do is almost always to alert the handler to specific sounds (such as smoke alarms) or to alert the handler to someone coming up from behind them.
The #1 side benefit reported is that the dogs serve as a "social bridge" to help people with deafness relate to others in their community. Almost 100% of the handlers said that they made more friends and were more social as a result of their service dog (this is an incredibly high result).
The journal, "Deaf Studies and Deaf Education" did a study that found that the handlers not only showed a large reduction in hearing-related problems(!), but the handlers also had:
A decrease in tension, anxiety, and depression
An increase in social involvement and independence
Another study found that:
Having a Hearing Service dog reduced their dependency on other people
A service dog for a deaf person reduced the hours of paid assistance needed
Concluded that hearing assistance dogs have a major positive impact on their handlers.
77% of people with hearing service dog reported that "It is easier to leave my home with my service dog", and hearing service dogs were found to help:
Activities of Daily Living (ADLs), such as chores, self-care, and mobility in the home and community
The study concluded that getting a hearing service dog would help a person who is deaf:
"(1) be healthier, (2) be more physically independent, (3) function better, (4) be more mobile, (5) participate more in productive activities, and (6) be more satisfied with life."
While some people with disabilities cannot work, many people with deafness do have jobs and they do their jobs well--and a Hearing Service Dog that can be taken to work and has been found to help both employee and their employer. While there are challenges to bringing a hearing service dog to work, a study concluded that the many benefits of having a service dog at work outweigh any potential barriers.
 "Hearing Dogs: A Longitudinal Study of Social and Psychological Effects on Deaf and Hard-of-Hearing Recipients," Claire M. Guest, along with Glyn M. Collis and June McNicholas.
 "Effects of assistance dogs on persons with mobility or hearing impairments," Diana H. Rintala, PhD; Rebeca Matamoros, BS; and Laura L. Seitz.
 "An Exploratory Study of the Elements of Successful Service Dog Partnerships in the Workplace," Margaret K. Glenn.