daf bit: Zevachim 8
The rabbis taught: the Pesach offering in its season, if slaughtered in its own name (that is, for that specific purpose, after being set aside for that purpose), is a valid offering, but if it was set aside and is then slaughtered for some other reason, it is invalid. During the rest of the year, however, if slaughtered in its name it is invalid, but if slaughtered for another reason it is valid. (8b)
Since a Pesach sacrifice isn't valid at other times of year it makes sense that it would be invalid if so designated, but the talmud here seems to be saying that if you set aside an animal for Pesach and then didn't use it, you can "reuse" it for another purpose if you wait until after Pesach. (That's how I read the footnote in Soncino, anyway.) Normally, as I understand it, if you designate something for a particular (holy) usage you can only use it for that purpose. But the conversation here is kind of confusing and I could be wrong; anyone who can clarify, please do so.

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The way I'm reading this (and Rashi references a more detailed discussion on Pesachim 60b-61a), a korban pesach is considered a subset of shlamim, and so even if it can't be offered as a korban pesach any more, once the window has closed it reverts to being designated for a shlamim in general.
But I could well be wrong.
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My Hebrew isn't good enough: is the Pesach korban to be specifically a lamb (implies a certain age) and not a sheep? Because if not, waiting until next year to offer it wouldn't be unreasonable. We always talk about lambs and they may be more practical in general; just wondering if there's actually a restriction there.