While NASA does not have any plans to send a specific missions to study the Oort Cloud, the most distant region in our solar system containing trillions of frozen objects, it has already sent five spacecraft in that direction. Two Voyager spacecraft, two Pioneer spacecraft, and the New Horizons spacecraft are all heading that way, but it is quite a distant.
For example, the Voyager spacecraft will not hit the Oort Cloud for another 300 years and will continue to travel through the cloud for another 30,000 years before escaping the solar system. As a result, all of these spacecraft will be dead as a rock before ever hitting that region and of no use to anyone back here, yet they will still carry messages from all of us to the stars. So in that sense, they still have a mission to perform should anyone be out there.
The Oort Cloud is still a theory since it has not been observed, but there is plenty evidence regarding its existence, including the comets that come into the center of our solar system from that region. The cloud itself is believed to be a sphere rather than on the same plane as the planets, so it forms a protective ring around the planets potentially becoming a hazard to any incoming or outgoing spacecraft. What this will mean for interstellar space travel, should that day come, is anyone’s guess at this point.
You can read more about the Oort Cloud here.