That almost never happens. I can count on one hand the number of times it has happened in ~100 past assessments. Generally speaking, the maxim, "There is no such thing as a secure system" is valid. Competent security consultants should be capable finding
something actionable in all but the most exceptional circumstances if you throw them into a room to search for vulnerabilities for a few weeks.
That said, I have had assessments where there were no findings. This is generally because there are informational observations that can't be escalated to vulnerabilities in the given assessment time, or because the application has a very security-conscious development team. If it happens, it might be a sign that the application is not sufficiently mature to require an assessment yet, or it's just too simple to really analyze. It can also mean that the consultant is not sufficiently competent to perform the assessment.
To give an example, I worked at a large consultancy where we had a giant public company hold us on retainer to perform assessments on "brochure websites" - they were not interactive at all. There wasn't even a login interface. The company wanted to check off that it had security assessments performed on all webpages it hosted, but realistically there were never any actionable findings. (This is about as much detail as I can give because it's NDA'd, but it's not the sort of thing I'd take on in my own practice).
A more recent example is a YC company I worked with a few weeks ago. Their development team is very well educated on security matters. While I found security vulnerabilities, there were no high severity findings because the quality of peer review and paranoid development was very high there. They were very familiar with every Ruby/Rails gotcha and pretty thoroughly avoided them.
To answer your question, I've never had anyone "angry" at me for not finding anything. They're not "happy", but as long as they can verify that the work they paid for was done, they aren't angry. It doesn't happen often, and when it has happened the consultant should provide enough information to demonstrate that competent work was done.
However, I personally don't feel very good about it. My understanding is that competent security engineers in general are not happy about it. It is much more likely that the assessment either shouldn't have happened (because the application is not mature or complex enough) or that the consultant was simply insufficiently competent than that the application is really completely secure.