Also just to add, it's a very bad idea to start messing with under or overclocking if your system is unstable to begin with. When you say you've hit "some difficulties" lately, what does that mean?
Messing with voltages and frequency requires a systematic approaching: unless you really know what you're doing, the best approach is to change 1 setting then test extensively, change again -> more testing. That way as soon as you hit an issue, you know exactly which setting caused the problem. If the computer is unreliable or unstable to begin with, you're in a mess because you'll have no way to know where the issue is coming from.
In terms of a general response, the only real "con" for undervolting is potential stability issues if you push voltages down too low. As a basic principle, higher voltages make it possible to achieve higher frequencies (= clock speed = performance), but at the cost of power and heat. If a voltage is too low for the frequency the CPU/GPU is trying to run, transistors won't be able to switch quickly enough and you'll get errors, BSODs, lockups, etc. Just to be clear, these issues caused by insufficient voltage will NOT physically damage your processor, they just cause it to not return the correct values and your system doesn't cope with this (thus crashes, freezes, BSOD, graphical glitches, etc). So ideally, CPUs and GPUs will run at the lowest possible voltage for their given frequency (thus less heat and power), but with just enough voltage to keep everything completely stable. The issue for AMD, Intel, Nvidia, etc, is that no two processors behave identically, that's the silicone lottery, some will run higher frequencies at low voltages, others not so much. While all processors are tested, it doesn't make financial sense to spend hours and hours stress testing each and every chip to determine its particular eccentricities, and they can't afford to cut the voltage too low and release a chip that might possibly error out under particular workloads. So, they have to be fairly conservative with the voltages they set. Because of that, if you have a system that supports it and you're prepared to do the careful testing yourself, you can often find a lower stable voltage than that set by the manufacturer.
So yeah - TLDR, you're trading off lower heat and power draw for potential instability and lockups.
The issue with undervolting is that no amount of stress testing can ever guarantee you 100% stability. Case in point, I got to what I thought was a very stable OC on my GPU for 8 months. Played loads of different games with no issues whatsoever. But then I got Witcher 3 and it would crash within 5 minutes every time. Bumped up the voltage again slightly and it was fine. I don't know why Witcher 3 on my particular card seemed to need just that little bit more voltage than anything else, but it did. People who undervolt will sometimes hit the same thing - you think it's stable until you find a particular workload that undoes it. But if your system supports undervolting and you're prepared to accept the potential instability and having to adjust things in future, there's not really any other drawbacks.