I was always able to listen to my roku tv through my headphones, however, now the headphone jack/cable will not stay plugged in to the tv. When I plug in the headphone jack/cable, it just falls out. Is it possible that something broke inside the little hole for the jack/cable that is on the side of my tv? If so, how can it be fixed?
My guess, though, is that you'll have trouble getting much support from the manufacturer for this issue.
As @boogernose suggests you could access your Roku tv via the Roku app on a cellphone connected to your home network and use the app's remote listening provision through the phone's speaker or a headset plugged into the phone. This also gives you much more freedom to move around compared to earphones plugged into the tv. I use an old phone no longer in service with my phone service carrier for this.
Roku Streaming Stick +, 3810X, Ser YH0059427035, wifi - Samsung UN55ES6100
Roku Streaming Stick, 3600X, Ser 5S56D8240827, wifi - JVC EM37T