Do MDs really mean it when they say “come back if you change your mind” when you exit?

No usually not. Would be kind of dumb to reapply to a place you quit from imo

I don't think this is a rote thing that people always say when letting people go. I think it's something you would probably only say if you meant it to some extent, because otherwise it's awkward if someone asks for it and you say "sorry, bad timing, I didn't mean it."

Sounds like you have an appetite for going back, so one could always just reach back out to the boss for old time's sake, play it cool for a good bit, and then test the waters on a potential return. "Ah, how's business going? What verticals are you seeing action in?" Then if you're getting good vibes, you can start getting a bit more overt with things like "That's great. You sound busy. The team keeping up with everything?" and try to get back in the saddle again.

The situation is far from guaranteed to go in your favor, but not asking is not getting.

If you want to come back call back your MD and let him know that.

If they have headcount they’d probably prefer someone they know than a lateral hire.

I definitely had been open to catch up with prior MDs or managers from my prior groups that I had either worked or interned at

Reapplying to a prior group, guess it depends on how chill the group culture was from what I last remember 

Have seen multiple people return to their banking group. Some really disliked their PE firm and wanted to reset a bit, and some thought banking as a career was better for them. Generally if you are a strong performer you can come back pretty easily.

Good friend of mine left on good terms for F500 corp dev and went back to the same group a year later - it definitely happens but it's uncommon. Always good to leave on the right note, grass isn't always greener. Funny enough he left F500 corp dev because the culture was "too laid back" and didn't work enough hours (30-40)

Has happened 3 times in my office where someone left and came back (many years later, 4 months later and a year later). Door is definitely open if they say so.

I once rejected a BB offer then changed my mind to ask for it back and they let me take it. If you are good and you have good relationships you can go and do what you want.

I have seen many people come back to my bank.

They typically left for PE or corporate and they decided for various reasons (including some saying they found PE boring) that they wanted to come back.

Over the years, have also seen a number of "boomerang" senior bankers that went to another bank and came back -- believe that is pretty common as well.

Meh, maybe out of a few hundred profiles I have come across, I have seen 1 or 2 people occasionally return to their initial group, top performers would always be welcome and you’d know if you were a top performer or not when you departed your group
 

On the other spectrum, I have occasionally seen some folk who were laid off or fired and then went scrambling back to their firm with their tail between their legs when offered a back office job in a different division too. It’s a tough hiring market these days and some people think the grass is greenest at the place that laid them off. It’s uncommon but you see this type of move here and there as well with bottom performers

Lot of dumb comments here.

Absolutely 100%, you can come back to a place that says that. I know many people who have done just that. As an employer, you would always rather bet on an employee that you know has worked out in the past and can do the job than taking a chance on someone from the outside. A past employee people already know they can gel with the team and are competent. There are lots of reasons people quit or leave jobs that months or years later could not be the case. Just going through some common examples:

• A new employer might be really mean, stupid, or just have a culture problem and the employee who left realizes leaving was a mistake 
• An employee who left might do self discovery and realize they actually needed a 6 month vacation and after 6 months they are bored and miss their old job
• An employee who left might have a change in circumstances and realize they need to stay in that geography or come back to that geography or they need a higher paying role because they have a medical expense or something

Look, I get as a junior employee you find quitting a job very personal and feel like you are letting people down, but the reality is it’s a part of business and not personal. Generally people quit because they need a change in hours, work, location, or they find somewhere with better pay. A lot of these can change and there’s a lot of risk with going to work somewhere new. It’s this reason why everyone says, “don’t burn bridges” it’s glamorous to think about telling your MD he’s a shitbag and being a douche on the way out, but you never know what happens in life and it is nice to have the safety of knowing you can always go back to your old investment bank where you can do the job and get paid well (even if it’s a little miserable)