I heard from some one that it is asked not to offer that woman's
funeral who doesn't marry any man.
I personally never heard of this, it might be a cultural thing not a religious one.
However, with respect to marriage - Islam encourages all to marry especially if it will prevent sin:
So marry them with the permission of their people and give them their
due compensation according to what is acceptable. [They should be]
chaste, neither [of] those who commit unlawful intercourse randomly
nor those who take [secret] lovers. But once they are sheltered in
marriage, if they should commit adultery, then for them is half the
punishment for free [unmarried] women. This [allowance] is for him
among you who fears sin, but to be patient is better for you. And
Allah is Forgiving and Merciful.
There is no punishment for you if you are unmarried but otherwise chaste, however as having sexual desires is a natural part of life, it is encouraged for you to marry lest you fall into sin. Since marriage is made easy in Islam, it is not difficult to expect people to get married.
Keep in mind that family and extending the Islamic faith through progeny is encouraged.
And Allah Knows Best.