Pretty much any modulation scheme can be decoded in software (though not necessarily in real time) if you can record the signal in samples capturing sufficient information.
Recording the audio output of a receiver's (AM or FM) demodulator is not necessarily going to be sufficient, unless it's a modulation mode such as AFSK designed to be used with voice radios.
Much more common is to have a receiver which outputs narrowband signals in IQ format, by mixing the final IF with two phases of a local oscillator to produce an audio-range intermediate frequency, often centered at 0 Hz. This is not a demodulated signal, but a form of digital IF which is suitable for digital demodulation. By using two phases, you can tell the positive and negative frequency components apart.
Stereo sound cards happen to provide you with two input channels, so people have tried to use them for IQ sampling of narrowband signals, however the input circuits of most sound cards aren't good all the way down to zero frequency, so it's sometimes preferable to use a non-zero center frequency and mix down to 0 in the digital domain. At higher bandwidths the same techniques apply, only higher performance A/Ds are used, typically feeding into ASICs, FPGAs, or DSPs.
There have been a lot of amateur radio, hobbyist, and professional receivers built using audio-frequency IQ sampling over the past decade - some web searching will turn up many projects including demodulation software, much of it open source. You will also find that some of the receiver front ends are pretty simple - often just an oscillator, a digital bus switch as a mixer (!) and some op amps.