I can't really address the flight characteristics of a 737NG, but many aircraft lack performance capability to put themselves high enough to be in coffin corner...truly in coffin corner (where any increase in speed will cause a high speed buffet, and any decrease will cause a stall). Margins do decrease as one climbs higher, but no airliner or business aircraft is operating on a razor edge at altitude.
If an encounter with turbulence occurs which causes airspeed excursions such that buffet margins are encountered, then one maintains attitide, accepts altitude and airspeed excursions, and responds to any departures from controlled flight. This doesn't mean one lets control get away, but if one reaches a low speed condition to the point of a stall, then one reacts to the stall with a stall recovery. If one experiences a high speed upset to the point that adverse mach effects are encountered, then one performs a high speed upset recovery. These are standard recoveries that are part of any normal training regime.
Minor excursions require minor corrections in most cases; perhaps just pulling the power back slightly in the event of an overspeed condition, for example. Large excursions, particularly attitude and pronounced airspeed losses or increases, require bigger corrections.
So far as older aircraft...as an airplane ages, it's not granted greater tolerances or more latitude in what's allowed to slide by. When the aircraft rolls out the factory door, it's handed over with maintenance publications spelling out exactly what cable tensions, control rod end play, system limits, clearances, etc, are acceptable. At no time, even 10, 20 or 30 years later, or 80,000 hours later, can the airplane be operated outside those tolerances...so regardless of the hard life and age of the airplane, it's still got to be maintained within the same tolerances that it had the day it was born.
Low speed buffet is tempered by early warning using horns, airspeed indications, angle of attack indicators, stick shakers, and finally pushers...these occur before the critical angle of attack is reached. Some respond to trends in airspeed and angle of attack, others respond only to set A0A in degrees. Each system resets based on aircraft configuration (the stall speed and A0A changes with the deployment of flaps and slats or other leading edge devices, etc...and the aircraft warning systems change to reflect this based on configuration. What all of this has in common is that it warns of what's coming before adverse flight characteristics are encountered.
Deep stall characteristics aren't particular only to T-tailed aircraft. Control authority may be degraded with other horizontal stab configurations, too. Additionally, the use of power to aid in recovery or to slow the decay through increasing angle of attack may have little effect against the drag rise or degraded control authority. This is all really another subject entirely, as it's a condition that's departed well beyond buffet margins. However, allowing most large aircraft, in fact many turbojet airplanes, to degrade well into a stalled condition can put the airplane in a state where recovery may be difficult, very prolonged, or even impossible. The whole idea is to never let the aircraft go that far. The Lear has been used as an example several times now; a protracted stall maneuver in a LR35A may take 10,000' or more for recovery, where as a stall to the shaker or pusher under normal circumstances may result in little or no altitude loss if dealt with properly.
One doesn't simply "drop out" of flight when approaching buffet margins. These are points where adequate warning is given well before adverse conditions occur. An aircraft which is allowed to fly beyond these points by substantial degrees can be brought to a state where adverse flight characteristics can take place.