The fallacy of appealing to lack of proof of the negative is a type of logical fallacy of the following form:
"This exists because there is no proof that it does not exist."
Non-fallacious ways to prove something include the use of logical syllogisms and/or the incorporation of empirical observations. But it is not logical to argue that something exists simply because there is no proof to the contrary; one cannot say, "No one has proven that aliens do not exist. Therefore, based on that alone, they must exist, notwithstanding that I have no evidence that they do exist". Given (as it is above) that it was not proven that aliens do not exist, they might exist, but this alone does not prove them to exist.
Another common example is that, "A supernatural force must exist because there is no proof that it does not exist". However, the converse is also true, according to the Argument from Ignorance: One also cannot say that, "I have not seen proof that something supernatural exists, therefore a supernatural force cannot exist". Also, similar to the aliens in the above example, since no proof is available that this does not exist, it might exist, but this alone does not prove it to exist.