My understanding is lead-free solder is stronger (SAC305, don't use pure tin), but does tend to fail in fracture while SnPb solder tends to fail more gradually.
Yeah, this is a complete and utter failure of mechanical engineering -- PCB materials are strong and stiff enough for themselves, but they aren't meant for much load bearing, and a PCB with components definitely isn't good for high strain! Absolutely, put a metal bracket under the poor thing. Maybe even isolate it from the bracket's strain by using a few mounting points in the middle, or a secondary bracket or something like that (with a vibration dampener on the end(s), to deal with the effective sprung mass this creates).
Assembles for robust applications are often potted. This can range from a jelly consistency mainly for environmental protection (it will will still absorb quite some acceleration, as effectively the board is buoyant in the potting, distributing forces more evenly than hard points might), all the way to glass-hard materials that turn the circuit into a rigid brick. (Usually a hybrid approach is used in that case, where the circuit is conformal coated with something goopy to provide strain relief, then potted in harder or rigid material.)
If for some reason, strain must be applied to the PCB, you can still do some isolation to help it. For example, rout a three-sided box around a given subcircuit, so that only strain from the one connected side can deform it. Various flextures can be made by routing, which will take up quite a lot of PCB area of course, and greatly limit electrical routing too, but can be used to make limited spring-mass isolation and filtering structures.
What's neat is, isolation could be as simple as one or two routs, but I think there are very few instances where 1. that will be enough isolation to do the job, and 2. where the forces or mounting locations or component locations actually benefit from such a step. (A simple example might be, a screw mount that happens to be subject to a bending moment; slotting the PCB beside it allows local torsion, without bowing adjacent components (on the other side of the rout).)
And obviously, you are left with less structural PCB, so the permissible load goes down dramatically (or the strain goes up, or the resonant frequency goes too low, or..).
So, this is rarely done in practice I think. Consider this not so much as useful practice, but as interesting supporting information.
One place it is kind of common to see, is the precision (voltage or time) reference in some test equipment. Dave's made some videos showing examples. The reference circuit might be isolated on a two-axis flexture. That is, a pair of facing 'C' shaped routs, which nearly cut out a rectangle from the main PCB. The rectangle is thus able to twist against the PCB plane, and isolated from one axis of stretch. Two sets of these cuts, nested and rotated 90 degrees, makes a bit of a two-gimbal linkage, allowing both axes of stretching and bowing, and twist (shear), to be isolated from the inner section. The thermal conduction path is likewise greatly lengthened, so that the section can be ovenized for thermal as well as mechanical stability. The resulting mass-spring system may be prone to resonance, but this may be partially addressed with dampening material which also serves as thermal insulation.
Tim