Does this pad function solve the problem?
julia> pad(v,n) = (L = length(v) ;
[i <= L ? v[i] : zero(eltype(v)) for i in 1:n] )
pad (generic function with 1 method)
julia> pad(coeffs(p),5)
5-element Vector{Int64}:
-10
-3
1
0
0
pad(v,n) will return vector of length n with elements from v where valid and zero otherwise.
A similar function might exist in some library, or might be added as it sounds useful.