Basically, I'm trying to figure out a way to run my SM57 through my pedals. I ordered a chord online that's female XLR to male 1/4 inch jack, so that I could plug the xlr into the mic and the jack into the pedal. The cable had good reviews so I figured it would work. However, what I didn't realize until I got the chord is that the jack has two rings, so it's a stereo signal. From what i understand about the way the signal works, i figured this wouldn't be a problem, so I plugged it into my pedal, and plugged that into the amp. I didn't get a signal at all, so I just tried running it straight to the amp. Still no signal. Shouldn't this work? The ground would just connect with the ground, and I don't imagine it would short out with the right signal, while the left would connect with the... main one.. the non ground one. I don't know maybe I'm totally wrong. Is it just a bad cable?
Let's start with what's right (though likely by accident). The SM57 is a dynamic microphone not needing phantom power (otherwise the scheme would be doomed to failure without a separate phantom power provision) but having low impedance. Which (without signal buffering/amplification) implies very low signal strengths on circuits designed for high impendance inputs like guitar rigs.
XLR-to-TRS is a standard mapping, so this is likely correct as well. TRS-balanced to TS-mono is where things get murky. "Converting" an unbalanced signal into a balanced one by plugging a TS-mono plug into a TRS socket for symmetrical signals is what this scheme supports.
For the reverse conversion, the connections are not reliable enough. To make this work, you need an actual TRS socket. A TS socket more often than not will leave the ring unconnected rather than shorting it with the shield.
But before you crank out your soldering iron: you usually want that connection to actually be symmetrical in order to reduce the otherwise significant noise bleeding into the low energy of microphone signals. So even if you completed the circuits, you would have a low-level noisy signal to work with.
The solution here is a "DI box" for converting balanced microphone-level signals to unbalanced guitar-impedance signals. The passive ones usually contain a small transformer catering for balanced/unbalanced and the impedance mismatch. You'd connect this box with a short unbalanced TS cable to your pedals and use a balanced XLR cable for the bulk of your microphone/pedal connection (not much of a consideration when the pedal is right below the microphone but generally longer lines should be balanced).
Passive DI boxes can usually be used in either direction. You'll need a female->female XLR adapter or cable, of course, in order to employ your DI400P box for that purpose. The gain will be about 20dB. It's conceivable that this mode of operation will create an unbalanced signal with a higher impedance than working well with your amp: in the intended direction, a very high impedance would not be problematic. In that case you might need a DI with different specs. But it's worth trying first.
The answer to your actual question is yes, TRS (bal) can be plugged into TS (unbal) and will effectively just become a TS connection.
But if your DI box doesn't sort you out, look for a HI-Z converter cable (female XLR to male 1/4"), which are made specifically for cases like this.
Anything along these lines should work. https://www.amazon.ca/Shure-A85F-Transformer-Female-4-Inch/dp/B0006NMUHW
The tube screamer uses a trs female jack to disconnects the ground from the power so that way you don’t drain the battery when you aren’t using the pedal. The sleeve of a male ts bridges what would be the ring and the sleeve and connects the ground. The problem you were most likely having is that since a 57 has a balanced output, that connection was never made. Try an xlr to ts. As far as I know you shouldn’t need a passive di because the first stage in the tubescreamer is a buffer.