I had heard that from Orthodox practice that a lady upon first marriage is expected to be a virgin and is represented as such, and that the couple are placed in a room right after the wedding to consummate the marriage immediately, and that then the relatives would soon after inspect the sheets for blood to verify that the consummation occured. But what happens to the couple's marital status or even the virgin's reputation if she fails to bleed upon defloration (for any number of possible physiological reasons)? Does she have to prick her own finger with a pin in case this happens?
The Biblical text:
And behold, he made libellous charges, saying, 'I did not find evidence of your daughter's virginity.' But this is the evidence of my daughter's virginity!' And they shall spread the garment before the elders of the city.
Rashi’s comment on “and they shall spread the garment”:
This is a figurative expression, meaning: they shall clarify the matter as [“clear”] as a [new] garment. — (Sifrei 22:92, Keth. 46a)
So what you describe is not Orthodox practice.
@Avrohom Yitzchok's answer gets to part of the misunderstanding here, but there is more to unpack.
1) A lady upon first marriage is expected to be a virgin.
So is the man. It isn't a particular virtue, it is just about where you naturally are if you are behaving correctly before marriage. In fact Rav Nachman in the Talmud says that if a previously unmarried man claims his bride was not a virgin, he is whipped, as he has shown that he was promiscuous before marriage. And the Talmud also says that man's misbehavior before marriage will cause the Sotah's bitter waters to not work.
All of this to say is that both the man and the woman are expected to be a virgin at their first wedding.
2) The couple are place in a room right after the wedding.
This is the Ashkanazic custom only. They have to be alone long enough that it could (theoretically) be consummated. However, no consummation actually takes place, it is a matter of finalizing the marriage. The couple typically breaks their fast (the bride and groom fast on the wedding day unless the day of the year prohibits fasting) and may kiss for the first time (although that isn't a formal requirement).
3) Relatives inspect the sheets
There is no such thing. As was said this is probably a completely taken out of context and misinterpreted reading of the verse there (even that doesn't discuss routine examination by the relatives, even if you read it literally).