The Laundry ball is a pseudoscientific product whose sellers claim that when placed in a washing machine, will clean clothes without detergent. The product is often sold by participants in multilevel marketing schemes.
Some of the pearl-based products claim to "generate powerful far infrared ray wave energy to cut off the hydrogen and binding of water molecule to have smaller water cluster to have the penetration and washing, at the same time, it radiates the anion electron to lower the surface tensile and interfacial tension for possible agent-free washing." (sic) . The claim of emitting infrared is not false, as all material emits "far infrared waves", in other words, heat radiation. It is also true that heating reduces the surface tension of water, but the effect of the radiation emitted by the pearls is negligible compared to the radiation emitted by the water which is being heated. There are no independent tests showing that the pearls could generate stronger infrared waves by interacting with water than what they otherwise should.
The claim of alkalization is dubious, while it is true that the alkaline agents in normal washing powders catalyze the tensides, there are no studies suggesting that the washing pearls would affect the pH of the water.
Many products also claim that the pearls contain "Anti-chlorine" agents which are supposed to neutralize chlorine which has been added to the tap water. Chloride and bleach related substances are actually common in washing powders and chlorine is used in the disinfection of tap water. The claims state that by removing chlorine from the washing water the surface tension is (again) reduced and harmful chlorine can't interact with the clothes, even though the amounts in tap water are very small both in Europe (0,3-1,0 ml/l) and North-America (4 ml/l).
Chlorine is a strong antibacterial agent, so neutralizing it from the washing water is illogical. There are no clear explanations of how the antibacterial substitute in the pearls work. A viable option would be silver pearls, as silver has documented antibacterial properties.
Some products claim to have magnetic elements which "minimizes the size of the water molecule which helps with scale and rust removal of the washing machine and pipes". Both of the claims are false from a proven scientific viewpoint: magnets do not interact with rust and molecules can't be "scaled" freely.