The correct way of doing it is reporting it as a bug to the manufacturer of the application, but that's probably not the answer you were looking for.
First, check that the resolution of your eMac isn't set to some stupidly low value, like 640*480. That can happen when using games. 1024*768 is probbaly the smallest it should be to work well. The eMac supports up to 1280*960, and most people seem to use that resolution. You set the resolution in the System Preferences application (under the Apple Menu) in OS X and in the Displays or Monitors control panel in OS 9 and below.
If the resolution is fine and it still won't work, you can fix it with Applescript. Open the application and make sure that the offending window is the one in front. Now open the Script Editor (it's in Applications/AppleScript in OS X - I think it's in the same place in OS 9, but search for it if you can't find it) and paste the following snippet of code into the window:
tell application "name of application"
activate
set bounds of front window to {0, 50, 400, 200}
end tell
(replace "name of application" with the actual name of your application, but keep it in quotes). Run the script. This will make the window much smaller, and you can grab the resize widget to make it the size you'd like it to be.