Quick question about pitch accent

Hello everyone, quick question about pitch accent, I know that the following particle is high or low depending on the word, like for 赤い the next particle's should be high in pitch since it's Heiban. But what about words?

What I'm asking is, if the next word starts low on its own but the word that comes before it is Heiban, then should it start high?

Example:

赤い > LHH[H]

財布 > LHH[H]

赤い財布 > LHHLHH or LHHHHH ?

Here, there are no particles, just words, but does the rule still applies that the next syllable should start high or not?

Thanks in advance.