Application? If you are coming to us from later or more powerful consoles where such tricks are possible then not really as scope for background processes is rather limited. Homebrew can be compiled with a few more options.
For making cheats or other debugging then emulators or USB geckos (or clones and spinoffs thereof) tend to be weapon of choice
https://wiibrew.org/wiki/USB_Gecko
https://wiibrew.org/wiki/Debugging (does mentions some network options but it is less nice memory viewer that is almost real time and more serial output fired over it if the baseline homebrew is made with it in mind).