The first thing to understand is that scarcity exists; that is, individuals are never entirely satisfied; there is never a point where individuals want for nothing. But, individuals may have an elevated demand for future goods relative to goods in the present; the reasons for this (retirement, sending the newborn child to college one day, the expectation of superior future goods, ect) are entirely immaterial to the economist.
Next, when you save you are sacrificing present consumption in favor of future consumption. To consume in the present means to consume finished products. Thus savings necessarily means a lower demand for finished, i.e., consumer goods. But those resources that you have not consumed do not simply lie idle, nor will entrepreneurs continue to produce products that are demanded less (consumer goods) relative to other products (future goods) by the same degree. The saved resources are, therefore, transferred to other economic employments, namely to branches of production that do not produce the finished products, but rather produce the inputs that eventually go into the finished products. This is done via the financial system (financial intermediaries), and they are able to do this because savings takes the form of money, which, by definition, is perfectly liquid. But money is not savings; it only allows individuals (entrepreneurs) to exchange for resources that have not been consumed.
Thus, to save means to donate resources, which you could have consumed, to other economic employments. In return, you earn interest (because all individuals prefer current consumption to future consumption, all other things equal). Those recourses, which you have devoted to other productive endeavors, increase the supply of capital which increases the marginal productivity of labor (wages) and total production (wealth).
It is true that a 100% savings rate would collapse the economy, the same way that a 100% consumption rate would eventually end civilization, but such a condition, though conceivable, is impossible. If Robinson Crusoe saves everything he finds/produces, then he will die of starvation; if he consumes everything, then he will live in material depravation.
Your example only demonstrates the effects of extreme alterations in demand conditions within an economic system consisting of only two goods (where one good is the only good that can sustain life and is extremely perishable). It says nothing about the tenability or economic importance of savings. It’s a meaningless hallucination that yields absurd conclusions (first explicitly expressed by Silvio Gessell). But your argument is a very crude (if that) version of the Keynesian argument which also resembles a similar argument made by Wicksell; both have been thoroughly refuted.