Look up a term called "schwa" in Wikipedia or somewhere.
You're going technical here, yes, that situation happens a lot, and some "pro/pre" situations are perfect examples of it. Like, "professor".
That's also partially why most Chinese students' "believe" sounds so unbelievable, just so you know. Look it up, man. It's a phonetics thing.
Edit
Thanks to this fine gentleman above, who is also my favourite dish. "Schwa" involves more than just vowels, if you get a phonology book or something in detail at hand. Yes, I'm not sure if it's appropriate to call it "lenition" (+ "liasion") in this case.
You think about what happens once the vowel fades, to a ”pro/pre". The "r" stands out. So normally an "r" in a position like this would be pronounced as in "read", "rise", yes? But now that the vowel's gone, the "r" plays a role similar to "doctor", "loner", ie what we call the "rhotic" thing, which most significantly happens the way around --- I weaR it vs I'm wea-Ring it. I mean just roughly explained like that, not in strict phonology, which is even more complicated.
Savy?