Maybe you could find something used with a $50 budget (?) but it's probably too low.
While wheels are turning, a few things to consider with the hardware are
1. Does the TV have an analog audio output? Some do, many don't. If it does, you could use that with most any amplifier or amplified speaker.
2. If the TV only has an optical digital output, does the TV setup menu allow you to configure it for stereo PCM output? Many do, some don't (Panasonic TVs have many models that don't allow you to set a stereo output).
If the output can't be set to stereo, then the digital input of an amplifier or speaker will have to be multi-channel Dolby Digital/DTS compatible, such as a soundbar or AV Receiver with digital input.
If you can find a pair of speakers really cheap, you might also be able to find an older cheap AV Receiver that provides a digital input and power to the speakers, but doesn't have HDMI inputs for video switching.
If you are buying new, you probably won't find anything for $50 and a $75 - $100 soundbar likely won't fill a larger room with sound with 2" - 3" drivers or provide any reasonable amount of bass without an external subwoofer.
Steve