Question

Food can spoil through mere exposure to air because it will lose electrons. This loss of electrons creates free radicals, which destroy chemical bonds in the food, causing it to spoil. What is this process called?

Answer 1

do you refer to the formation of the free radicals or to the spoilage of food by the formation of free radicals?
the last one can be also called Oxidation

the formation of free radicals
The formation of radicals may involve the breaking of covalent bonds by homolysis, a process that requires significant amounts of energy. Such energies are known as homolytic bond dissociation energies, usually abbreviated as "ΔH°". Splitting H2 into 2H•, for example, requires a ΔH° of +435 kJ·mol-1, while splitting Cl2 into 2Cl• requires a ΔH° of +243 kJ·mol-1.
The bond energy between two covalently-bonded atoms is affected by the structure of the molecule as a whole, not just the identity of the two atoms. Likewise, radicals requiring more energy to form are less stable than those requiring less energy. An additional barrier can be the selection rule. Propagation, however, is very exothermic.
Radical formation through homolytic bond cleavage most often happens between two atoms of similar electronegativity; in organic chemistry, this is often between the O–O bond in peroxide species or between O–N bonds. Radicals may also be formed by single-electron oxidation or reduction of an atom or molecule: an example is the production of superoxide by the electron transport chain. Early studies in organometallic chemistry – especially F. A. Paneth and K. Hahnfeld's studies of tetra-alkyl lead species during the 1930s – supported the heterolytic fission of bonds and a radical-based mechanism. Although radical ions do exist, most species are electrically neutral.

https://en.wikipedia.org/wiki/Radical_(chemistry)#Formation