かける: an action started but not finished
Read unfinished actions and moments on the verge of happening with the masu-stem plus かける. Compare 始める, the noun-modifying かけの form, and whether completion actually occurred.
Focusing on what remains unfinished
読みかけの本を机に置きました。 means that the speaker put a partially read book on the desk. Reading has begun but is not complete; it does not specifically mean exactly half the book has been read.
Remove ます from the masu-form and add かける, producing forms such as 読みかける and 食べかける. Before a noun, 食べかけのパン describes bread someone has started eating, unlike untouched bread.
On the verge or just beginning
何か言いかけて、やめました。 means that the speaker started or was about to say something, then stopped. 言いかける can capture the boundary before speech or its very beginning, so the intended message was not necessarily spoken in full.
Depending on context, かける can describe either an action underway but unfinished or a state just before an occurrence. Do not assume that every verb combined with it necessarily implies a completed portion of the action.
Comparing 始める with an unfinished state
本を読み始めました。 focuses on the fact that reading the book began. 読みかけの本があります。 presents a book whose reading remains incomplete.
書きかけた手紙を、翌日書き終えました。 describes finishing an incomplete letter the following day. Using かける once does not mean the action was abandoned forever; later context can supply its completion.
Quick check: If there is 食べかけのケーキ, has all the cake been eaten?
Show the answer and why
No. There is cake that someone has started but not finished eating. The expression does not specify exactly how much remains.