NR developed shake, and when bigger studios started using it, they wanted access to the source code. Disney was one customer who paid to put shake's source code into escrow, with a stipulation that if NR ever went under or got acquired, they could pull it out of escrow and build shake (on Linux) themselves.
Enter Steve Jobs and Apple, who viewed shake as an asset that could help push studios towards Mac OS X, and away from SGI and upstart Linux which was steadily taking SGI's high-end CG market. When Apple acquired Nothing Real, Steve wasn't at all happy with the animation studio's CTO who decided to exercise their contract and pull the shake code out of escrow.
Disney ported shake to amd64 Linux and continued to use and extend it all the way until Tangled (2008), and while it's not their main workhorse compositor these days, shake still runs today, despite Apple's best efforts to kill it ;-). To Apple's credit, they eventually realized that shake's source code was not really that big of an asset, so they offered a deal at one point where studios could pay (50k+?) to get access to the source code. Many studios payed.
Having compared the NR sources to the Apple sources, quite a bit of work was done to put in PPC-specific assembly and performance optimizations (e.g. optimizing for G5's cache sizes) into Darwin-specific #ifdefs.
One takeaway from this story is that the "big" customer (Disney) in this case was not at all interested in stealing IP. They were an animation studio and their core product was something not-software. If the customer in your case is in a closer space, it's a different calculus.
The customer's viewpoint was more of being able to decide their own fate in the event of the company going away. And it turns out, those things did happen, so having the deal in place was a good thing for the customer. Likewise, Nothing Real made out very well in all of this, as they got paid by Disney (among others), and later acquired by Apple who really didn't care enough about the pre-existing contracts to not acquire them.
One protection in the contract was that it only allowed for the studio to produce binaries for themselves, but not distribute them. A practical consequence of this is that Disney could not share shake binaries with Pixar, and while Pixar had also purchased a source license from Apple, Disney could only share (git format-patch) patches with Disney's changes. I really wish we could have open sourced the shake source code, even for historical purposes[2]. Apple still can.
Make sure the deal is reasonable and there shouldn't be any problems. If you don't trust the company then maybe you shouldn't take them on as a client, but otherwise a reputable company will be very willing to keep things as friendly as your lawyers can get them to be. Having a good lawyer is key.
Regarding copy-pasting your code -- in shake's case, having the source code was really helpful for plugin development. Maybe consider ways to help customers leverage actually having the source code. Making the system plugin-able is a great way to do that, as customers mostly want to customize stuff, and plugins are a great way to get customers "deeply integrated" (aka locked) into your ecosystem.
[1] https://en.wikipedia.org/wiki/Shake_(software)#History
[2] https://www.flickr.com/photos/ronbrinkmann/sets/721576179728...