Oil tanks, often neglected and tbh they dont usually cause too many issues but you would be surprised at how much gunk they can harbour. They are easiest to clean out after the saw has been ran for awhile as i warms the oil up so it pours out quicker and removes more gunk. Remove your oil cap and let the saw sit over a container, big plastic jugs work well. once its more or less drained out us an air line with a rag over the plug hole to blast the bits out, an other technique is to fill it with old fuel, swill it about pour out and repeat. Check the state of the oil filter, most Stihls have a very basic plastic filter that doesn't usually block but it can let a lot of bits of sawdust through, Husky filters are usually brass and can break apart and block the oil pipe. Echo's have a proper filter but they clog quicker.
Another thing to check is the oil tank breather vent, usually under a metal plate on the huskys and hidden behind the plastic guide rail on stihls. Differnt place son echos but usually underneath the starter cover. They let air in but stop oil coming out. If they block up it will create a vacuum in the oil tank and result in no oil to the bar.
IMO most oiling issues are caused by a worn drive or in the case with Stihls a worn or damaged worm driver, if you want to call it that. Its the metal piece that connects the worm to the clutch drum pictured here
Worm Gear - Stihl 1121 640 7111
SKYLANDEQUIPMENT.COM
Replacement worm gear for the Stihl chainsaws listed below. FITS CHAINSAW MODELS 026, 260, MS 261 OEM 11216407111 GENUINE STIHL PART YES MANUAL
Also dont forget to clean the oil hole out in the bar. If your chain isnt getting the right amount of oil it will cause plenty of cutting problems.
Last thought on this, oil pumps rarely fail, if you have tried the above and nothing helps and your oil pump has an adjuster try turning the adjuster back and forth as they can stick. Oil pumps are usually pricey, some not far off the £100 mark!