What is the fate of the typical tree?
This is a great question.
Without going into too much detail, there is a series of studies done in northeastern US temperate forests (specifically at Great Mountain Forest in Connecticut, USA) on the growth, survival, and dispersal of canopy trees. In this particular community, light appears to be the primary limiting factor. Seedlings and saplings in low-light environments (i.e. stuck under the canopies of mature trees) grow slowly and have poor carbon balance, which makes them susceptible to mortality (probably from pathogens, although the proximal cause of death of seedlings and saplings is rarely known). Early successional tree species (in GMF, white ash/red maple/red and white oak) grow especially slowly, and hence are more likely to die, in low-light conditions; late successional (hemlock and beech) grow slowly even in high light, but are tolerant of slow growth, so are likely to survive until the adult tree above them dies and falls down.
The exact answer to &quot;at what point do these trees die&quot; is a little tricky, but here's a figure from Kobe et al. showing estimated survival probability for different species as a function of light availability (the assumption is of independent mortality probabilities, given light availability, at each time step, so there is no particular stage at which individuals die in the model).



Kobe, Richard K., Stephen W. Pacala, John A. Silander Jr, and Charles D. Canham. “Juvenile Tree Survivorship as a Component of Shade Tolerance.” Ecological Applications 5, no. 2 (1995): 517–532.
Pacala, Stephen W., Charles D. Canham, John Saponara, John A. Silander Jr, Richard K. Kobe, and Eric Ribbens. “Forest Models Defined by Field Measurements: Estimation, Error Analysis and Dynamics.” Ecological Monographs 66, no. 1 (1996): 1–43.
Pacala, Stephen W., Charles D. Canham, and John A. Silander Jr. “Forest Models Defined by Field Measurements: I. The Design of a Northeastern Forest Simulator.” Canadian Journal of Forest Research 23, no. 10 (1993): 1980–1988.
Pacala, Stephen W., Charles D. Canham, John A. Silander Jr, and Richard K. Kobe. “Sapling Growth as a Function of Resources in a North Temperate Forest.” Canadian Journal of Forest Research 24, no. 11 (1994): 2172–2183.