OPTION 1
As Catholics, we are accustomed to having religious objects "blessed," which signifies the permanent sanctification and dedication of an object for some sacred purpose. Once a religious object is blessed and dedicated for divine worship or veneration, it must be treated with reverence and must not be used in either an improper or profane way (cf. Code of Canon Law, #1171).
What happens when the rosary or statue breaks and is irreparable? Or, when the palm dries out, and the following Palm Sunday provides us with new palm? The basic rule for the disposition of these items is to burn or to bury them.
Therefore, the normal "rule of thumb" is that anything that has been blessed should be burned (and then the ashes buried) or simply buried.
OPTION 2
As a Catholic, collecting sacramentals such as votive candles, religious pictures, rosaries (which sometimes break), medals, palm branches and other misc. religious items is fairly common. What do you do if you are unsure if they are blessed?
One option, if they are still useable, is to give them away to other people who could use them. If you can’t find any takers there are other options.
Respectful disposal
The proper disposal of votive candles and other devotionals, if they have been blessed, is to burn or to bury them, most preferably the former in the case of candles. Letting candles burn down entirely, or, if this presents a hazard should the glass candle holders break, burn them by themselves.
It is not a sin to throw away blessed items, but out of proper respect, one should dispose of them in this way. If devotionals have not been blessed, such as some of the holy cards and such that come through the mail, those are simply pictures and can be thrown away.
If you feel uncomfortable throwing them away, you can burn or bury them as well.
OPTION 3
SHOULD NOT BE SHARED:
--Any liturgical items that are obviously damaged or worn beyond their ability to function worthily.
• If the items are burnable, they should be burned. If possible, the ashes should then be collected and buried on church grounds or in a Catholic cemetery.
• If the items cannot be burned they should be disassembled or destroyed in a way that prevents any profane re-use and then buried on church grounds or in a Catholic cemetery—not disposed of in a landfill. If the item is metal that could be melted-down for re-use it must first be disassembled or destroyed in a way that prevents any profane re-use in its recognizable form prior to its trip to the smelter.
When attempting to burn textiles:
• A hot fire already burning with its own fuel source is required.
• It may be best to throw any textile items on the already burning fire one-by-one, as some textiles are treated to specifically inhibit burning. (A thick pile of them thrown-on at once may not ignite and may even extinguish the fire.)
• Stay away from the fumes given off by the burning textiles as they may be somewhat toxic.
When attempting to burn hardcover books: