First things first: starting in precalculus is not necessarily a dealbreaker, but it almost certainly means that an engineering degree is no longer a 4-year endeavor. Having to retake precalculus means that is even more certain.
That said, failing precalculus in the first semester is not necessarily a dealbreaker in an academic sense. Students struggle early in a variety of classes, even “easy” and important ones, for a variety of reasons that may not necessarily say anything about that student’s viability as an engineer. Perhaps the stress of adjusting to living more independently hurt this student’s grades. Perhaps they were poorly prepared from high school either in terms of study habits or in terms of background knowledge and had a lot of catching up to do. Perhaps they really just couldn’t handle it. The point is that it’s hard to pinpoint a reason, and that reason is key to determining if engineering is a realistic career path. Failing it a second time would essentially be a dealbreaker in my opinion.
However, the issue is that precalculus is such a low level class that retaking it could set the student back an entire year, meaning that, realistically, completing an engineering degree is now all but guaranteed to take a minimum of 5 years. Is that a financially-viable plan for this student and their family? I can’t really answer that. It may be an option to save a little money and take precalculus at a community college and then go back to paying the full tuition at a 4-year university again once the student can hit the ground running rather than wasting a lot of time taking irrelevant courses due to the fact that the prerequisites for higher courses are not yet complete. This is particularly a problem when it comes to calculus, because, while professors are often willing to waive prerequisites in some cases (for example, if a student is just starting dynamics, I am willing to let them enroll in fluid mechanics anyway), they generally won’t waive that for calculus because a student would be utterly lost without it.
So really, this is an issue that the student must sort out with his or her family. Does the potential reward justify the risk and financial investment required to move forward from here.