Lots of interesting things can happen! What happens to an electron after it leaves an atom can depend on what caused it to leave. Electrons are normally happy to stay near an atom/within a material because they are attracted to the positively charged nuclei of the atom.

Sometimes an electron can leave an atom because the atom forms a chemical bond to another atom. Bonds that form because an atom loses an electron are called ionic bonds. An ionic bond forms when one atom loses an electron to give it to the other. This is the kind of bonding that holds compounds like table salt (NaCl) together.

Some more exciting ways an electron can leave an atom occur when a lot of energy is dumped into a material. Near an atom, electrons sit at specific energies in atomic orbitals, but if the electron gains a bunch of energy, it gets ejected from the atom. Sometimes it will stay within the material, but now it's able to move around because it has gained energy. Sometimes the electron can even fly away from the material at high speeds! Scientists from all kinds of fields of study take advantage of these effects and purposefully excite electrons to study materials. For example, when Albert Einstein explained the photoelectric effect, where light of specific wavelengths/energies can eject electrons from a material, he kickstarted the study of quantum mechanics and revolutionized physics. Nowadays, similar techniques can be used to study atoms, their bonds, and much more so we can understand why atoms and electrons behave in interesting ways in different materials.

In a solid state material, if an element loses an electron, this electron can be transferred to another atom, or simply "wander around" in the system as a free electron and contribute to electric current in electric cable.

When thinking of this question, always remember positive and negative charges attract each other and prefer to be close in order to maintain a neutral charge

. So if an element loses an electron, it will be because something made that electron "prefer" to be somewhere else. One possibility is that a more energetically favorable (so here let's say positively charged) atom is nearby. In this instance, the electron would travel to the new atom. Often in this case, the electron does not completely leave, but rather forms a bond between the atoms, making a molecule! Another alternative is that a force can be applied that "rips" the electron away.

Think of ripping tape of a wall- the tape was perfectly happy to stick to the wall, but if you pull hard enough, it will come off and stick to a new place where your force directs it. For electricity (i.e. electrons) this force is called an electric potential (or voltage), if the voltage is high enough for the given species, electrons will be encouraged to leave their current atoms and travel to the next place they can stick, typically another atom that can hold onto electrons at that given voltage.

The electron leaps onto something else. In a salt crystal of NaCl, the electron from the Na sticks to the Cl, so in water it is Na+ and Cl-, covered with water molecules.

In dry air we can sometimes get static electricity that transfers a bit of electric charge to some material. Sometimes when I take the thin plastic wrapping off something, the plastic sticks to my hand because there are a few electrons that got separated from a few positive charges when I pulled the plastic off the thing it was wrapped around.

Where the electron goes depends on under what condition the atom loses the electron. If the atom loses an electron while forming a bond with another atom, the "lost" electron is now part of the other atom. Note that this type of bond is most often defined as an ionic bond because in covalent bonds, atoms do not lose electrons to each other; they share their electrons with each other. An electron can also be lost during radioactive decay, and the electron lost in this process is called a beta minus particle. The beta minus particle has very high energy and will hit surrounding atoms and molecules until it loses enough energy, at which point it will likely become a free floating electron in the environment. (An important distinction here is that the electrons that atoms lose during the formation of chemical bonds are electrons that orbit the atomic nucleus, whereas electrons ejected during radioactive decay come from the nucleus.

During bond formation, the atom stays as its original element; during radioactive beta decay, the element changes to another element.)

The electron either becomes a free electron, or it becomes part of another atom. The only way to destroy an electron is to annihilate it with a positron.