You would typically first read from the input stream and then close it. You can wrap the FileInputStream in another InputStream (or Reader). It will be automatically closed when you close the wrapping stream/reader.
If this is a method returning an InputStream to the caller, then it is the caller's responsibility to close the stream when finished with it. If you close it in your method, the caller will not be able to use it.
To answer some of your comments...
To send the contents InputStream to a remote consumer, you would write the content of the InputStream to an OutputStream, and then close both streams.
The remote consumer does not know anything about the stream objects you have created. He just receives the content, in an InputStream which he will create, read from and close.