The best way I can characterize it is it sounds like something in the chain is getting a weak signal and sending it to the amp. I ran into this a lot when I was into home theater: pro-audio amps combined with consumer-level AVRs, most of which couldn't output a strong enough signal.
That's not really specific enough to be helpful, mostly because a weaker line signal is not always absolutely detrimental. A couple of examples:
First there was one audio show before where one manufacturer basically trolled everybody as to the source unit feeding the amplifier that was driving gigantic speakers. They put a CDP on there, everybody was liking the sound, and then they told everybody that the line signal was actually coming from an iPod. Even on its proper line out (via the LOD 30-pin cable) it's 1.2V, well below Redbook standard for single ended output (not that balanced output is specified in the Redbook; AFAIK it isn't).
Second, I have a portable DAC-HPamp with a 1.2V line out here that I use as a DAC with my laptops (Win7 before and Win10 now) because somehow my back-up desktop DAC-HPamp's USB receiver+DAC chip has extremely buggy Windows drivers (but even weirder is that none of my Androids even need UAPP), and the problem isn't distortion but output level vs noise. Since the output level is low given the weaker signal it has to work with, I have to get to 1:00 on the dial, and the audible noise is there. Using its own USB DAC which sends out 2V, if I pause the music and move the dial, the noise becomes audible at 1:00 too, except I can't test it with music running because with the 2V signal I'm deaf by 12:00. The closest it gets to "distortion" is that the bass is weaker with the portable DAC-HPamp's line output into the desktop amp even at 1:00 on the dial, or even 2:00,
but without actually measuring the output at the bass frequencies, it's far more likely that I'm just not hearing the bass right because the noise is there.
In either case the amp or preamp having a higher gain setting can make up for that weaker signal provided the amp actually still has enough power to handle how much louder you want it to go running off a weaker line signal.
Basically the line input to the amp and the amp's input sensitivity has to be low enough to really distort the bass
if the problem is due to a weak line signal. Otherwise other reasons are more likely:
1. The amp is distorting for another reason, like low sensitivity or too low impedance of the transducers it is driving for its output voltage or current delivery
2. The DAC's line output signal isn't flat
3. A perfect storm of the above reasons, like the NuForce Icon HDP having overexcursion with the HD600 when using USB input. While normally weaker DAC-HPamps don't even have that problem, they're not boosting the low end either, something I noticed when the same HDP's preamp output was hooked up to a power amp driving towers vs a DACMagic they had on hand.
4. A too hot signal instead of a too weak one, like when I had the SuperPro 707 DAC that pulls power via USB, as well as utilize a more powerul power brick, according to some forum posts, so I tried a different power brick. My Little Dot Mk2 had ear pounding distorted bass where there's a bass-y humming following notes and it was literally painful to listen to. Some guy measured it and the output was more like 6.5V in that configuration - basically the same output level as Pioneer car audio receivers cranked up to the hilt by people using them to drive 1000w ++++ mono Class D amplifiers to either win a trophy or look cool when their windshield cracks or the roof makes coins jump. When I used the SuperPro 707 via SPDIF and a regular power brick, there were zero problems.
