Some scriptures on the question:
I Timothy 5:8
If anyone does not provide for his relatives, and especially for his immediate family, he has denied the faith and is worse than an unbeliever.
Leviticus 5:7, 11
If he cannot afford a lamb, he is to bring two doves or two young pigeons to the LORD as a penalty for his sin - one for a sin offering and the other for a burnt offering. But if his means suffice not for two turtle-doves, or two young pigeons, then he shall bring his oblation for that wherein he hath sinned, the tenth part of an ephah of fine flour for a sin-offering: he shall put no oil upon it, neither shall he put any frankincense thereon; for it is a sin-offering.
Le 12:8 If she cannot afford a lamb, she is to bring two doves or two young pigeons, one for a burnt offering and the other for a sin offering. In this way the priest will make atonement for her, and she will be clean.
Notice that pigeons around here are wild, and probably were back then too. If someone did not own livestock for the sacrifice, they could capture one from the wild. Maybe I have this wrong, but that is how it appears.
Lev. 14:
21
If, however, he is poor and cannot afford these, he must take one male lamb as a guilt offering to be waved to make atonement for him, together with a tenth of an ephah
F31 of fine flour mixed with oil for a grain offering, a log of oil, and two doves or two young pigeons, which he can afford, one for a sin offering and the other for a burnt offering.
32 These are the regulations for anyone who has an infectious skin disease and who cannot afford the regular offerings for his cleansing
Le 27:8
If anyone making the vow is too poor to pay the specified amount, he is to present the person to the priest, who will set the value for him according to what the man making the vow can afford.
Nu 6:21
This is the law of the Nazirite who vows his offering to the Lord in accordance with his separation, in addition to whatever else he can afford. He must fulfill the vow he has made, according to the law of the Nazirite.'" Lev. 27:31
A tithe of everything from the land, whether grain from the soil or fruit from the trees, belongs to the LORD; it is holy to the LORD.
If a man redeems any of his tithe, he must add a fifth of the value to it.
De 14:23 Eat the tithe of your grain, new wine and oil, and the firstborn of your herds and flocks in the presence of the LORD your God at the place he will choose as a dwelling for his Name, so that you may learn to revere the LORD your God always. (There are several instructions for enjoying certain offerings... not each type, but specified ones.)
De 14:24 But if that place is too distant and you have been blessed by the LORD your God and cannot carry your tithe (because the place where the LORD will choose to put his Name is
so far away)...
De 26:12 When you have finished setting aside a tenth of all your produce in the third year, the year of the tithe,
you shall give it to the Levite, the alien, the fatherless and the widow, so that they may eat in your towns and be satisfied.