The laws of Borer-Removing a solid from within a liquid:
Small solids: Small solids retain all the Borer restrictions with regards to removing them from liquid or vice versa. Thus, separating small pieces of onion, chicken, vegetables from soup contains the Borer restrictions. Likewise, removing a fly or hair from a liquid contains the Borer restrictions.
Large solids: Solid pieces, which are large and thus individually recognizable from amongst the liquid, are not considered a mixture with the liquid and the Borer restrictions thus do not apply. However, this only applies if the solid that one wants to remove is not mixed with other solids, as in such a case, if one desires to select one solid from amongst another, the Borer restrictions would apply, as the solids are considered a mixture with each other, irrelevant of the liquid. Examples:
Vegetable or chicken soup: One may remove a Matzah ball, large piece of potato or large piece of meat from soup without following the Borer restrictions so long as there is only one species of solid within the soup. Alternatively, if one desires to remove all the solids from the soup, then if all the solids are large, one may remove it from the soup without Borer restrictions.
- One may remove a hardboiled egg from within water.
- One may remove a tea bag from tea. However, one must use a spoon to do so in order to prevent any dripping of tea from the bag back into one’s cup.
- One may remove a rice bag from amongst the chulent [although according to some Poskim one is to do so in a way that the gravy from within the bag not drip into the chulent in the process of removing it, such as through removing it with a spoon.]
Cans? Regarding removing the solid from the liquid inside of a can, If the food that is within the can is in small enough pieces to be defined as mixed together with the liquid, then the separating restrictions apply. However, if the liquid only contains large solid foods, then it is not defined as mixed with the liquid and thus none of the separating restrictions apply.
- Canned whole pickles/sardines/eggplant: Are not defined as mixed and thus may have their liquid removed in any which way.
- Canned cut pieces of pickles/sardines/eggplant: Are defined as mixed and thus retain all the separating restrictions explained.
- Canned olives: Are defined as mixed and thus retain all the separating restrictions.
- Canned Tuna: Is defined as mixed and thus retains all the separating restrictions.
 See Shevisas Hashabbos Borer 18; Ketzos Hashulchan 125 footnote 14 and 126 footnote 19; Az Nidbaru 4/21; Shabbos Kihalacha Vol. 2 p. 211; Piskeiy Teshuvos 319/17; Nishmas Adam 179
 So is proven from Admur 319/24; Admur in Siddur; Taz 319/13; 506/3; M”B 319/61 and all Poskim who discuss the methods of removing a fly from a soup in a way that will not transgress the Borer restrictions.
 Shevisas Hashabbos Borer 18; Ketzos Hashulchan 125 footnote 14 and 126 footnote 19; Az Nidbaru 4/21; Shabbos Kihalacha Vol. 2 p. 211; Piskeiy Teshuvos 319/17; Nishmas Adam 179; See however Kaneh Bosem 3/19 regaridng pickels in a can
 Meaning, that they are the only solids in the liquid. Such as soup which contains only Matzah balls, or only potatoes, and cases of the like.
 Shabbos Kehalacha Vol. 2 p. 212