IIR based lowpass filters (probably the most common kind in music software) introduce a phase delay around the filtering frequency. To demonstrate I did this in my audio application using a steep lowpass filter. I used a well-tested commercial VST plugin for this test:
Create some white noise at -6 dB.
Make a copy of the generated white noise (using copy/paste instead of generating new noise.)
Apply a steep lowpass filter at 1000 Hz to this copy (e.g. 24 or 36 dB/oct.)
Make a new file containing a mix of the original plus the lowpass filtered audio (100% + 100%).
Also, make another new file containing a mix of the original minus the lowpass filtered audio (100% - 100%).
Analyze the frequency spectrum of the results.
The lowpass filtered audio
Mixed (filtered + original)
The result clearly shows the surprising outcome, which in most cases is an unwanted effect. The noise now sounds like it's been through a long tube. This is not because of a problem with the lowpass filter i chose, but a result of physics and matematics. This is why you rarely see lowpass and highpass filters offering a wet/dry mix button.