TeX emergencystretch retry leaves unacceptable paragraph breakpoints unresolved

TeX's Knuth–Plass paragraph builder retries breakpoint selection once with \emergencystretch after \pretolerance and \tolerance passes fail. The goal is to confirm whether that single emergencystretch attempt is the engine's final fallback when no acceptable breakpoints exist, or whether an additional automatic retry is available in any TeX engine.

Documented behavior indicates that TeX issues an overfull or underfull box instead of retrying with more stretch, and offers no built-in per-paragraph switch to disable emergencystretch or iterate beyond one retry. This policy appears stable across Knuth TeX, pdfTeX, XeTeX, and LuaTeX core line breaking, although microtype and font expansion in extended engines can alter badness outcomes. Version assumptions cover these four engines without claiming engine-specific extensions beyond the documented pass sequence.

Does TeX treat emergencystretch as the final line-breaking attempt before emitting an overfull or underfull box?

Is there an engine-level mechanism in pdfTeX, XeTeX, or LuaTeX to request another breakpoint retry after emergencystretch fails without manual rewording?

When breakpoints remain unacceptable, is local parameter grouping or rewording the only documented remedy?