You mean 1'', don't you? Anyhoo, stinkbugs and other 6,8, and zillion legged creatures find their way into our homes fairly frequently. Some are looking for a place to overwinter; others are looking for moisture and snacks. Some get in by accident...like the Japanese beetle that came in on the back of my husband's T-shirt last summer. We've both brought in lightning bugs by accident after sitting on the back patio for the evening.

Since you mention ONE stink bug, I'd not worry about it for a millisecond. Flush it when you catch it.

How, or why, depends on many things starting with where you are. Up here we have had numerous encounters with Box Elder Bugs and the Asian Lady Beetles because they find shelter in the out side walls of the house and migrate inward during warmer winter days. Very few of these overwintering insects eat, or drink, much of anything.
Adult Stink Bugs are known to overwinter in many areas of the country, usually outside under garden debris. I would not find it inconcievable that some, on warm winter days, would become active and move around, or that some might have found a way inside your house like the Box Elder and Lady Beetles do.