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Jen the following example sentences.

Mi povas venki la <kion ajn>, sen tio, ke vi min {helpas,helpus,helpu}!
Mi povas venki la <kion ajn>, per[e de] tio, ke vi min {helpas,helpus,helpu}!

I could very well have simply said "sen via helpo" or "per[e de] via helpo", or even reorder the clauses for clarity, but that would be besides the point of the question. Just wondering what moods the "helpi" can take when in a subordinate clause after a "sen tio" or "per tio".

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Via demando estas tre detale respondita en PMEG ĉe Verboformoj en ke-frazoj. Vi trovos tie multajn ekzemplojn.

Resume:

  • se la ĉeffrazo kaj la ke-frazo estas facile disigeblaj, oni uzu la saman verboformon

Laŭ la tipo de ke-frazo:

  • cela: oni uzu la volan (-u) modon

  • opinia: oni uzu realan modon (-is, as, -os). Tamen volan modon oni povas uzi se temas pri nerealaĵo.

  • ebla: oni uzu realan modon -is, -as, -os).

  • imaga: oni uzu imagan (-us) modon

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PMEG 12.3.6.12 gives a general rule, that "sen estas la malo de kun kaj iafoje la malo de per". For ke-frazoj Wennergren adds "sed normale oni intermetas helpan tio" and gives an example

Via patro neniam povis ekrigardi vin sen tio, ke li batus sin en la bruston kaj ĝemus [Rt40*]

(Your father can never look upon you without forging his chest and moaning. (my Google translation into English))

I think, that the logic goes the following way. Because sen means absence, lack i.e. the "tio" never happens, the subclause is imaginary i.e. use the us-modo.

Furthermore PMEG 33.2.3 lists some cases, where you can leave the "tio" out before an explaining subclause. These are

  • por ke
  • malgraŭ ke
  • anstataŭ ke
  • krom ke
  • sen ke

Note, that it is not wrong to use "tio" with these. So

  • Mi povas venki ion ajn sen (tio), ke vi min helpus.

Based on my native language I prefer without, but you may prefer otherwise.

*: Rt40 = La Rabistoj de Friedrich Schiller tradukis de L. L. Zamenhof, p. 40

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  • What about in the inverse case of "per", especially if the "tio" has yet to happen? Would this then still be in the conditional, for the reason you mentioned, or in the volitive this time? My guess is still us-modo, as the "tio" is not necessarily a celo, but instead something that would make the main clause realized.
    – Mona the Monad
    Commented Jul 13, 2020 at 15:52
  • I think, that Eduardo's answer covers the general case. I didn't found any "per ke" in Tekstaro and "per tio ke" only from 1991 onwards. At a glance they seem to be of "opinion type", i.e. oni uzu la realan modon as Eduardo said.
    – Juha Metsäkallas
    Commented Jul 13, 2020 at 16:34
  • I took a new look at the examples of use of per tio ke in Tekstaro. Quite a many seems to correspond to the English "by that (it means/favours/implies/…"). Given that the Eo prepositions should usually be understood rather literally (e.g. per should be used to denote a tool or a method), it seems more and more to me, that per tio ke is mostly used in an erroneous fashion.
    – Juha Metsäkallas
    Commented Jul 14, 2020 at 8:29

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