Being an unofficial helper verb,
かけ is what is known as a 造語（ぞうご） (neologism), and carries one specific meaning when used in conjunction with other words. This is similar to
向（む）け.
かけ comes from the verb 掛（か）ける ‘to suspend’, and may be attached to the 連用形（れんようけい） (conjunctive form) or other verbs, in order to convey that they are ‘unfinished’. Usually this translates as ‘half (A)’, ‘about to (A)’, or ‘not yet finished (A)’.
かけ behaves like a noun, so may be followed by the 格助詞（かくじょし） (case marking particle) の when attached directly to another noun, or by
だ when at the end of a sentence.
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俺（おれ）の食（た）べかけだけど大丈夫（だいじょうぶ）？
This is half-eaten by me, is that okay?
これは私（わたし）の飲（の）みかけだ。
This is my half-drunken one.
彼（かれ）は死（し）にかけの子犬（こいぬ）を救（すく）った。
He saved a puppy that was about to die. (Half dead)
彼女（かのじょ）は壊（こわ）れかけのパソコンを買（か）って直（なお）すのが趣味（しゅみ）だ。
Her hobby is to buy half-broken computers and fix them. (Computers on the verge of breaking)
Occasionally, the verb 掛（か）ける itself may be used instead of the noun form,
かけ.
-
やばい、死（し）にかけるところだった。
Wow, I was about to be dying right there. (Almost on the verge of dying)
飲（の）みかけた水（みず）を捨（す）てる。
I will throw away my half drunk water.
As the literal meaning of 掛（か）ける is ‘to suspend’, it expresses that something is stuck somewhere in the process of happening. This is similar to taking a photo of someone that is jumping. In the photo it will look like they are ‘suspended’, but that is only because one particular moment has been captured, somewhere between the start and the finish.
かけ conveys exactly the same meaning, and therefore may be interpreted differently, depending on the verb it is paired with.
With verbs that express a momentary action (something that cannot be ‘half’ done),
かけ will convey that the action was ‘on the verge of’ happening.
-
先週（せんしゅう）の事故（じこ）で死（し）にかけそうになった。
I was on the verge of dying in an accident last week.
壊（こわ）れかけていた椅子（いす）に座（すわ）ったら、椅子（いす）が壊（こわ）れた。
When I sat on a chair that was on the verge of breaking, it broke.
However, with verbs that are ongoing actions,
かけ will simply imply that they are ‘in the process’ of being done.