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Inbreeding is mostly not very good because when there is a 'disease' in one allele, the other could/would take over the function. But when you have two of the same genes/alleles, do they, or could they have advantages? Can inbreeding be beneficial?

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Certainly it is not necessarily the case that having two of the same allele is a bad thing - if there is a "bad" allele then there is a "good" allele. It can be that the heterozygote is equal, better than, or worse than either homozygote. When the heterozygote is fitter than both homozygotes it is called heterosis and, when this is the case, outbreeding/hybridisation is advantageous.

The process of inbreeding can actually improve fitness because it increases the rate at which deleterious mutations (bad mutations) are expressed, and therefore the efficacy of selection. If the population avoids fatal inbreeding depression it can have positive effects. This process of removing deleterious variants by inbreeding is called genetic purging.

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    $\begingroup$ A good example of homozygotes being more fit might be Polled Cattle. The allele that makes horns on cattle is actually recessive, so a cow needs two copies to have horns. A cow with horns is better able to defend itself in the wild. It also allows them to outcompete other cattle for food on the farm, and can be a safety issue for the farmer. By breeding bulls to be homozygous for the dominant no-horns allele, you can easily remove horns from a herd and avoid costly, and potentially harmful, surgical horn removal. $\endgroup$
    – user137
    Commented Jun 8, 2016 at 10:33
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The phrasing in quite unclear and I would not be able to comment on it.

In short: yes, hybridization can cause offspring to have either particularly low or particularly high fitness. Hybrid depression refers to cases where hybrids have low fitness while heterosis or hybrid vigour refers to cases where hybrids have a higher fitness than any of the two parent lines.

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